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day-of-year
Combined from primary sources listed below.

In role Dateish§

See primary documentation in context for method day-of-year. 

method day-of-year(Date:D: --> Int:D)

Returns the day of the year (1..366).

say Date.new('2015-12-31').day-of-year;                                  # OUTPUT: «365␤»
say DateTime.new(date => Date.new('2015-03-24'), hour => 1).day-of-year; # OUTPUT: «83␤»