Date::ISO8601 - the three ISO 8601 numerical calendars

Date-ISO8601 documentation Contained in the Date-ISO8601 distribution.

Index

Code Index:

NAME

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Date::ISO8601 - the three ISO 8601 numerical calendars

SYNOPSIS

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	use Date::ISO8601 qw(present_y);

	print present_y($y);

	use Date::ISO8601
		qw(month_days cjdn_to_ymd ymd_to_cjdn present_ymd);

	$md = month_days(2000, 2);
	($y, $m, $d) = cjdn_to_ymd(2406029);
	$cjdn = ymd_to_cjdn(1875, 5, 20);
	print present_ymd(2406029);
	print present_ymd(1875, 5, 20);

	use Date::ISO8601
		qw(year_days cjdn_to_yd yd_to_cjdn present_yd);

	$yd = year_days(2000);
	($y, $d) = cjdn_to_yd(2406029);
	$cjdn = yd_to_cjdn(1875, 140);
	print present_yd(2406029);
	print present_yd(1875, 140);

	use Date::ISO8601
		qw(year_weeks cjdn_to_ywd ywd_to_cjdn present_ywd);

	$yw = year_weeks(2000);
	($y, $w, $d) = cjdn_to_ywd(2406029);
	$cjdn = ywd_to_cjdn(1875, 20, 4);
	print present_ywd(2406029);
	print present_ywd(1875, 20, 4);

DESCRIPTION

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The international standard ISO 8601 "Data elements and interchange formats - Information interchange - Representation of dates and times" defines three distinct calendars by which days can be labelled. It also defines textual formats for the representation of dates in these calendars. This module provides functions to convert dates between these three calendars and Chronological Julian Day Numbers, which is a suitable format to do arithmetic with. It also supplies functions that describe the shape of these calendars, to assist in calendrical calculations. It also supplies functions to represent dates textually in the ISO 8601 formats. ISO 8601 also covers time of day and time periods, but this module does nothing relating to those parts of the standard; this is only about labelling days.

The first ISO 8601 calendar divides time up into years, months, and days. It corresponds exactly to the Gregorian calendar, invented by Aloysius Lilius and promulgated by Pope Gregory XIII in the late sixteenth century, with AD (CE) year numbering. This calendar is applied to all time, not just to dates after its invention nor just to years 1 and later. Thus for ancient dates it is the proleptic Gregorian calendar with astronomical year numbering.

The second ISO 8601 calendar divides time up into the same years as the first, but divides the year directly into days, with no months. The standard calls this "ordinal dates". Ordinal dates are commonly referred to as "Julian dates", a mistake apparently deriving from true Julian Day Numbers, which divide time up solely into linearly counted days.

The third ISO 8601 calendar divides time up into years, weeks, and days. The years approximate the years of the first two calendars, so they stay in step in the long term, but the boundaries differ. This week-based calendar is sometimes called "the ISO calendar", apparently in the belief that ISO 8601 does not define any other. It is also referred to as "business dates", because it is most used by certain businesses to whom the week is the most important temporal cycle.

The Chronological Julian Day Number is an integral number labelling each day, where the day extends from midnight to midnight in whatever time zone is of interest. It is a linear count of days, where each day's number is one greater than the previous day's number. It is directly related to the Julian Date system: in the time zone of the prime meridian, the CJDN equals the JD at noon. By way of epoch, the day on which the Convention of the Metre was signed, which ISO 8601 defines to be 1875-05-20 (and 1875-140 and 1875-W20-4), is CJDN 2406029.

This module places no limit on the range of dates to which it may be applied. All function arguments are permitted to be Math::BigInt or Math::BigRat objects in order to achieve arbitrary range. Native Perl integers are also permitted, as a convenience when the range of dates being handled is known to be sufficiently small.

FUNCTIONS

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Numbers in this API may be native Perl integers, Math::BigInt objects, or integer-valued Math::BigRat objects. All three types are acceptable for all parameters, in any combination. In all conversion functions, the most-significant part of the result (which is the only part with unlimited range) is of the same type as the most-significant part of the input. Less-significant parts of results (which have a small range) are consistently native Perl integers.

All functions die if given invalid parameters.

Years

present_y(YEAR)

Puts the given year number into ISO 8601 textual presentation format. For years [0, 9999] this is simply four digits. For years outside that range it is a sign followed by at least four digits.

This is the minimum-length presentation format. If it is desired to use a form that is longer than necessary, such as to use at least five digits for all year numbers (as the Long Now Foundation does), then the right tool is sprintf (see sprintf in perlfunc).

This format is unconditionally conformant to all versions of ISO 8601 for years [1583, 9999]. For years [0, 1582], preceding the historical introduction of the Gregorian calendar, it is conformant only where it is mutually agreed that such dates (represented in the proleptic Gregorian calendar) are acceptable. For years outside the range [0, 9999], where the expanded format must be used, the result is only conformant to ISO 8601:2004 (earlier versions lacked these formats), and only where it is mutually agreed to use this format.

Gregorian calendar

Each year is divided into twelve months, numbered [1, 12]; month number 1 is January. Each month is divided into days, numbered sequentially from 1. The month lengths are irregular. The year numbers have unlimited range.

month_days(YEAR, MONTH)

The parameters identify a month, and the function returns the number of days in that month as a native Perl integer.

cjdn_to_ymd(CJDN)

This function takes a Chronological Julian Day Number and returns a list of a year, month, and day.

ymd_to_cjdn(YEAR, MONTH, DAY)

This performs the reverse of the translation that cjdn_to_ymd does. It takes year, month, and day numbers, and returns the corresponding CJDN.

present_ymd(CJDN)
present_ymd(YEAR, MONTH, DAY)

Puts the given date into ISO 8601 Gregorian textual presentation format. The `extended' format (with "-" separators) is used. The conformance notes for present_y apply to this function also.

If the date is given as a (YEAR, MONTH, DAY) triplet then these are not checked for consistency. The MONTH and DAY values are only checked to ensure that they fit into the fixed number of digits. This allows the use of this function on data other than actual Gregorian dates.

Ordinal dates

Each year is divided into days, numbered sequentially from 1. The year lengths are irregular. The years correspond exactly to those of the Gregorian calendar.

year_days(YEAR)

The parameter identifies a year, and the function returns the number of days in that year as a native Perl integer.

cjdn_to_yd(CJDN)

This function takes a Chronological Julian Day Number and returns a list of a year and ordinal day.

yd_to_cjdn(YEAR, DAY)

This performs the reverse of the translation that cjdn_to_yd does. It takes year and ordinal day numbers, and returns the corresponding CJDN.

present_yd(CJDN)
present_yd(YEAR, DAY)

Puts the given date into ISO 8601 ordinal textual presentation format. The `extended' format (with "-" separators) is used. The conformance notes for present_y apply to this function also.

If the date is given as a (YEAR, DAY) pair then these are not checked for consistency. The DAY value is only checked to ensure that it fits into the fixed number of digits. This allows the use of this function on data other than actual ordinal dates.

Week-based calendar

Each year is divided into weeks, numbered sequentially from 1. Each week is divided into seven days, numbered [1, 7]; day number 1 is Monday. The year lengths are irregular. The year numbers have unlimited range.

The years correspond to those of the Gregorian calendar. Each week is associated with the Gregorian year that contains its Thursday and hence contains the majority of its days.

year_weeks(YEAR)

The parameter identifies a year, and the function returns the number of weeks in that year as a native Perl integer.

cjdn_to_ywd(CJDN)

This function takes a Chronological Julian Day Number and returns a list of a year, week, and day.

ywd_to_cjdn(YEAR, WEEK, DAY)

This performs the reverse of the translation that cjdn_to_ywd does. It takes year, week, and day numbers, and returns the corresponding CJDN.

present_ywd(CJDN)
present_ywd(YEAR, WEEK, DAY)

Puts the given date into ISO 8601 week-based textual presentation format. The `extended' format (with "-" separators) is used. The conformance notes for present_y apply to this function also.

If the date is given as a (YEAR, WEEK, DAY) triplet then these are not checked for consistency. The WEEK and DAY values are only checked to ensure that they fit into the fixed number of digits. This allows the use of this function on data other than actual week-based dates.

SEE ALSO

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Date::JD, DateTime

AUTHOR

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Andrew Main (Zefram) <zefram@fysh.org>

COPYRIGHT

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Copyright (C) 2006, 2007, 2009, 2011 Andrew Main (Zefram) <zefram@fysh.org>

LICENSE

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This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

Date-ISO8601 documentation Contained in the Date-ISO8601 distribution. 
package Date::ISO8601;

{ use 5.006; }
use warnings;
use strict;

use Carp qw(croak);

our $VERSION = "0.004";

use parent "Exporter";
our @EXPORT_OK = qw(
	present_y
	month_days cjdn_to_ymd ymd_to_cjdn present_ymd
	year_days cjdn_to_yd yd_to_cjdn present_yd
	year_weeks cjdn_to_ywd ywd_to_cjdn present_ywd
);

# _numify(A): turn possibly-object number into native Perl integer

sub _numify($) {
	my($a) = @_;
	return ref($a) eq "" ? $a : $a->numify;
}

# _fdiv(A, B): divide A by B, flooring remainder
#
# B must be a positive Perl integer.  A may be a Perl integer, Math::BigInt,
# or Math::BigRat.  The result has the same type as A.

sub _fdiv($$) {
	my($a, $b) = @_;
	if(ref($a) eq "Math::BigRat") {
		return ($a / $b)->bfloor;
	} else {
		if($a < 0) {
			use integer;
			return -(($b - 1 - $a) / $b);
		} else {
			use integer;
			return $a / $b;
		}
	}
}

# _fmod(A, B): A modulo B, flooring remainder
#
# B must be a positive Perl integer.  A may be a Perl integer, Math::BigInt,
# or Math::BigRat.  The result has the same type as A.

sub _fmod($$) {
	my($a, $b) = @_;
	if(ref($a) eq "Math::BigRat") {
		return $a - $b * ($a / $b)->bfloor;
	} else {
		return $a % $b;
	}
}


sub present_y($) {
	my($y) = @_;
	my($sign, $digits) = ("$y" =~ /\A\+?(-?)0*([0-9]+?)\z/);
	$digits = ("0" x (4 - length($digits))).$digits
		unless length($digits) >= 4;
	$sign = "+" if $sign eq "" && length($digits) > 4;
	return $sign.$digits;
}


sub _year_leap($) {
	my($y) = @_;
	return _fmod($y, 4) == 0 &&
		(_fmod($y, 100) != 0 || _fmod($y, 400) == 0);
}

{
	my @month_length = (31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31);
	sub month_days($$) {
		my($y, $m) = @_;
		croak "month number $m is out of the range [1, 12]"
			unless $m >= 1 && $m <= 12;
		if($m == 2) {
			return _year_leap($y) ? 29 : 28;
		} else {
			return $month_length[$m - 1];
		}
	}
}

{
	my @nonleap_monthstarts =
		(0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334, 365);
	my @leap_monthstarts =
		(0, 31, 60, 91, 121, 152, 182, 213, 244, 274, 305, 335, 366);
	sub _year_monthstarts($) {
		my($y) = @_;
		return _year_leap($y) ?
			\@leap_monthstarts : \@nonleap_monthstarts;
	}
}


sub cjdn_to_yd($);

sub cjdn_to_ymd($) {
	my($cjdn) = @_;
	my($y, $d) = cjdn_to_yd($cjdn);
	my $monthstarts = _year_monthstarts($y);
	my $m = 1;
	while($d > $monthstarts->[$m]) {
		$m++;
	}
	return ($y, $m, $d - $monthstarts->[$m - 1]);
}


sub yd_to_cjdn($$);

sub ymd_to_cjdn($$$) {
	my($y, $m, $d) = @_;
	croak "month number $m is out of the range [1, 12]"
		unless $m >= 1 && $m <= 12;
	$m = _numify($m);
	my $monthstarts = _year_monthstarts($y);
	my $md = $monthstarts->[$m] - $monthstarts->[$m - 1];
	croak "day number $d is out of the range [1, $md]"
		unless $d >= 1 && $d <= $md;
	$d = _numify($d);
	return yd_to_cjdn($y, $monthstarts->[$m - 1] + $d);
}


sub present_ymd($;$$) {
	my($y, $m, $d);
	if(@_ == 1) {
		($y, $m, $d) = cjdn_to_ymd($_[0]);
	} else {
		($y, $m, $d) = @_;
		croak "month number $m is out of the displayable range"
			unless $m >= 0 && $m < 100;
		croak "day number $d is out of the displayable range"
			unless $d >= 0 && $d < 100;
	}
	return sprintf("%s-%02d-%02d", present_y($y),
		_numify($m), _numify($d));
}


sub year_days($) {
	my($y) = @_;
	return _year_leap($y) ? 366 : 365;
}

use constant GREGORIAN_ZERO_CJDN => 1721060;   # 0000-001


sub cjdn_to_yd($) {
	my($cjdn) = @_;
	use integer;
	my $d = $cjdn - GREGORIAN_ZERO_CJDN;
	my $qcents = _fdiv($d, 365*400 + 97);
	$d = _numify($d - $qcents * (365*400 + 97));
	my $y = $d / 366;
	my $leaps = ($y + 3) / 4;
	$leaps -= ($leaps - 1) / 25 unless $leaps == 0;
	$d -= 365 * $y + $leaps;
	my $yd = year_days($y);
	if($d >= $yd) {
		$d -= $yd;
		$y++;
	}
	return ($qcents*400 + $y, 1 + $d);
}


sub yd_to_cjdn($$) {
	my($y, $d) = @_;
	use integer;
	my $qcents = _fdiv($y, 400);
	$y = _numify($y - $qcents * 400);
	my $yd = year_days($y);
	croak "day number $d is out of the range [1, $yd]"
		unless $d >= 1 && $d <= $yd;
	$d = _numify($d);
	my $leaps = ($y + 3) / 4;
	$leaps -= ($leaps - 1) / 25 unless $leaps == 0;
	return (GREGORIAN_ZERO_CJDN + 365*$y + $leaps + ($d - 1)) +
		$qcents * (365*400 + 97);
}


sub present_yd($;$) {
	my($y, $d);
	if(@_ == 1) {
		($y, $d) = cjdn_to_yd($_[0]);
	} else {
		($y, $d) = @_;
		croak "day number $d is out of the displayable range"
			unless $d >= 0 && $d < 1000;
	}
	return sprintf("%s-%03d", present_y($y), _numify($d));
}


# _year_phase(YEAR): find day of week of first day of year
#
# The argument must be a native Perl integer.  The return value is
# zero-based, in the range 0 = Monday to 6 = Sunday.

sub _year_phase($) {
	my($y) = @_;
	return yd_to_cjdn($y, 1) % 7;
}

sub year_weeks($) {
	my($y) = @_;
	$y = _numify(_fmod($y, 400));
	my $phase = _year_phase($y);
	return $phase == 3 || ($phase == 2 && _year_leap($y)) ? 53 : 52;
}


sub cjdn_to_ywd($) {
	my($cjdn) = @_;
	my($y, $d) = cjdn_to_yd($cjdn);
	my $py = _numify(_fmod($y, 400));
	my $phase = _year_phase($py);
	my $start_wk1 = ($phase <= 3 ? 1 : 8) - $phase;
	my $w = _fdiv($d - $start_wk1, 7);
	if($w == -1) {
		$y--;
		$w = year_weeks($py - 1);
	} elsif($w >= year_weeks($py)) {
		$y++;
		$w = 1;
	} else {
		$w++;
	}
	return ($y, $w, ($d - $start_wk1) % 7 + 1);
}


sub ywd_to_cjdn($$$) {
	my($y, $w, $d) = @_;
	my $yw = year_weeks($y);
	croak "week number $w is out of the range [1, $yw]"
		unless $w >= 1 && $w <= $yw;
	croak "day number $d is out of the range [1, 7]"
		unless $d >= 1 && $d <= 7;
	my $start_cjdn = yd_to_cjdn($y, 1);
	my $phase = _fmod($start_cjdn, 7);
	return $start_cjdn +
		(($phase <= 3 ? -8 : -1) - $phase +
			_numify($w)*7 + _numify($d));
}


sub present_ywd($;$$) {
	my($y, $w, $d);
	if(@_ == 1) {
		($y, $w, $d) = cjdn_to_ywd($_[0]);
	} else {
		($y, $w, $d) = @_;
		croak "week number $w is out of the displayable range"
			unless $w >= 0 && $w < 100;
		croak "day number $d is out of the displayable range"
			unless $d >= 0 && $d < 10;
	}
	return sprintf("%s-W%02d-%d", present_y($y), _numify($w), _numify($d));
}


1;