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Ordinal date : ウィキペディア英語版
Ordinal date
An ordinal date is a calendar date typically consisting of a ''year'' and a ''day of year'' ranging between 1 and 366 (starting on January 1), though year may sometimes be omitted. The two numbers can be formatted as YYYY-DDD to comply with the ISO 8601 ordinal date format.
==Calculation==
Computation of the ordinal date within a year is part of calculating the ordinal date throughout the years from a reference date, such as the Julian date. It is also part of calculating the day of the week, though for this purpose modulo-7 simplifications can be made.
For these purposes it is convenient to count January and February as month 13 and 14 of the previous year, for two reasons: the shortness of February and its variable length. In that case the date counted from 1 March is given by
:floor ( 30.6 ( ''m'' + 1 ) ) + ''d'' − 122
which can also be written
:floor (30.6 ''m'' − 91.4 ) + ''d''
with ''m'' the month number and ''d'' the date.
The formula reflects the fact that any five consecutive months in the range March–January have a total length of 153 days, due to a fixed pattern 31–30–31–30–31 repeating itself some more than twice.
"Doomsday" properties:
For ''m'' = 2''n'' and ''d''=''m'' we get
:floor (63.2 ''n'' − 91.4 )
giving consecutive differences of 63 (9 weeks) for ''n'' = 2, 3, 4, 5, and 6, i.e., between 4/4, 6/6, 8/8, 10/10, and 12/12.
For ''m'' = 2''n'' + 1 and ''d''=''m'' + 4 we get
:floor (63.2 ''n'' − 56.8 )
and with ''m'' and ''d'' interchanged
:floor (63.2 ''n'' − 56.8 + 118.4 )
giving a difference of 119 (17 weeks) for ''n'' = 2 (difference between 5/9 and 9/5), and also for ''n'' = 3 (difference between 7/11 and 11/7).
The ordinal date from 1 January is:
*for January: ''d''
*for February: ''d'' + 31
*for the other months: the ordinal date from 1 March plus 59, or 60 in a leap year
or equivalently, the ordinal date from 1 March of the previous year (for which the formula above can be used) minus 306.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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