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#### 8.5.3 Business Days

Often time is measured in “business days” or “working days,” where weekends and holidays are skipped. Calc's normal date arithmetic functions use calendar days, so that subtracting two consecutive Mondays will yield a difference of 7 days. By contrast, subtracting two consecutive Mondays would yield 5 business days (assuming two-day weekends and the absence of holidays).

The `t +` (`calc-business-days-plus`) [`badd`] and `t -` (`calc-business-days-minus`) [`bsub`] commands perform arithmetic using business days. For `t +`, one argument must be a date form and the other must be a real number (positive or negative). If the number is not an integer, then a certain amount of time is added as well as a number of days; for example, adding 0.5 business days to a time in Friday evening will produce a time in Monday morning. It is also possible to add an HMS form; adding ‘`12@ 0' 0"`’ also adds half a business day. For `t -`, the arguments are either a date form and a number or HMS form, or two date forms, in which case the result is the number of business days between the two dates.

By default, Calc considers any day that is not a Saturday or Sunday to be a business day. You can define any number of additional holidays by editing the variable `Holidays`. (There is an `s H` convenience command for editing this variable.) Initially, `Holidays` contains the vector ‘`[sat, sun]`’. Entries in the `Holidays` vector may be any of the following kinds of objects:

- Date forms (pure dates, not date/time forms). These specify particular days which are to be treated as holidays.
- Intervals of date forms. These specify a range of days, all of which are holidays (e.g., Christmas week). See Interval Forms.
- Nested vectors of date forms. Each date form in the vector is considered to be a holiday.
- Any Calc formula which evaluates to one of the above three things. If the formula involves the variable ‘`y`’, it stands for a yearly repeating holiday; ‘`y`’ will take on various year numbers like 1992. For example, ‘`date(y, 12, 25)`’ specifies Christmas day, and ‘`newweek(date(y, 11, 7), 4) + 21`’ specifies Thanksgiving (which is held on the fourth Thursday of November). If the formula involves the variable ‘`m`’, that variable takes on month numbers from 1 to 12: ‘`date(y, m, 15)`’ is a holiday that takes place on the 15th of every month.
- A weekday name, such as `sat` or `sun`. This is really a variable whose name is a three-letter, lower-case day name.
- An interval of year numbers (integers). This specifies the span of years over which this holiday list is to be considered valid. Any business-day arithmetic that goes outside this range will result in an error message. Use this if you are including an explicit list of holidays, rather than a formula to generate them, and you want to make sure you don't accidentally go beyond the last point where the holidays you entered are complete. If there is no limiting interval in the `Holidays` vector, the default ‘`[1 .. 2737]`’ is used. (This is the absolute range of years for which Calc's business-day algorithms will operate.)
- An interval of HMS forms. This specifies the span of hours that are to be considered one business day. For example, if this range is ‘`[9@ 0' 0" .. 17@ 0' 0"]`’ (i.e., 9am to 5pm), then the business day is only eight hours long, so that `1.5 t +` on ‘`<4:00pm Fri Dec 13, 1991>`’ will add one business day and four business hours to produce ‘`<12:00pm Tue Dec 17, 1991>`’. Likewise, `t -` will now express differences in time as fractions of an eight-hour day. Times before 9am will be treated as 9am by business date arithmetic, and times at or after 5pm will be treated as 4:59:59pm. If there is no HMS interval in `Holidays`, the full 24-hour day ‘`[0 0' 0" .. 24 0' 0"]`’ is assumed. (Regardless of the type of bounds you specify, the interval is treated as inclusive on the low end and exclusive on the high end, so that the work day goes from 9am up to, but not including, 5pm.)

If the `Holidays` vector is empty, then `t +` and `t -` will act just like `+` and `-` because there will then be no difference between business days and calendar days.

Calc expands the intervals and formulas you give into a complete list of holidays for internal use. This is done mainly to make sure it can detect multiple holidays. (For example, ‘`<Jan 1, 1989>`’ is both New Year's Day and a Sunday, but Calc's algorithms take care to count it only once when figuring the number of holidays between two dates.)

Since the complete list of holidays for all the years from 1 to 2737 would be huge, Calc actually computes only the part of the list between the smallest and largest years that have been involved in business-day calculations so far. Normally, you won't have to worry about this. Keep in mind, however, that if you do one calculation for 1992, and another for 1792, even if both involve only a small range of years, Calc will still work out all the holidays that fall in that 200-year span.

If you add a (positive) number of days to a date form that falls on a weekend or holiday, the date form is treated as if it were the most recent business day. (Thus adding one business day to a Friday, Saturday, or Sunday will all yield the following Monday.) If you subtract a number of days from a weekend or holiday, the date is effectively on the following business day. (So subtracting one business day from Saturday, Sunday, or Monday yields the preceding Friday.) The difference between two dates one or both of which fall on holidays equals the number of actual business days between them. These conventions are consistent in the sense that, if you add n business days to any date, the difference between the result and the original date will come out to n business days. (It can't be completely consistent though; a subtraction followed by an addition might come out a bit differently, since `t +` is incapable of producing a date that falls on a weekend or holiday.)

There is a `holiday` function, not on any keys, that takes any date form and returns 1 if that date falls on a weekend or holiday, as defined in `Holidays`, or 0 if the date is a business day.