Rata Die is a system for assigning numbers to calendar days, independent of any calendar, for the purposes of calendrical calculations. It was named by Howard Jacobson. The same system was used earlier, e.g., the REXX programming language since about 1980:
The base date of 1 January 0001 is determined by extending the current Gregorian calendar backward.
Rata Die is somewhat similar to Julian Dates, in that the values are plain real numbers that increase by 1 each day. The systems differ principally in that JD takes on a particular value at a particular absolute time, and is the same in all contexts, whereas R.D. values may be relative to time zone, depending on the implementation. This makes R.D. more suitable for work on calendar dates, whereas JD is more suitable for work on time per se. The systems also differ trivially by having different epochs: R.D. is 1 at midnight local time on January 1, AD 1 in the proleptic Gregorian calendar, JD is 0 at noon Universal Time on January 1, 4713 BC in the proleptic Julian calendar, and the REXX count of days begins with 0 at midnight local time on January 1, AD 1 in the proleptic Gregorian calendar.
Forms
Dershowitz and Reingold
There are three distinct forms of R.D. In this section they will each be defined in terms of Julian Dates. The first form of R.D. is a continuously-increasing fractional number, taking integer values at midnight local time. It may be defined in terms of the Julian Date as In the second form, R.D. is an integer that labels an entire day, from midnight to midnight local time. This is the result of rounding the first form of R.D. downwards. It is the same as the relation between Julian Date and Julian Day Number. Thus: In the third form, the R.D. is an integer labelling noon time, and incapable of labelling any other time of day. This is defined as where the R.D. value must be an integer, thus constraining the choice of JD. This form of R.D. is used in the book for conversion of calendar dates between calendars that separate days on different boundaries. The book does not explicitly distinguish between these three forms, using the abbreviation "R.D." for all of them. The book does not say that the RD is based on Greenwich time, but page 10 states that an R.D. with a decimal fraction is called a moment, and the function moment-from-jd takes a floating point number as an argument and returns the argument -1721424.5; there is no requirement or opportunity to supply a time zone offset as an argument.
REXX
The DATE function of the REXX computer language can return the number of complete days since and including the base date, 1 January AD 1 Gregorian, if the "Base" option is specified. This function uses local, not Greenwich, time. REXX does not use the name "Rata Die".
