The Functions (code, formulas, and calendar data) contained in this book were written by Nachum Dershowitz and Edward M. Reingold (the “Authors”), who retain all rights to them except as granted in the License and subject to the warranty and liability limitations below. These Functions are subject to this book's copyright.

In case there is cause for doubt about whether a use you contemplate is authorized, please contact the Authors.

1. 1. LICENSE.The Authors grant you a license for personal use. This means that for strictly personal use you may copy and use the code and keep a backup or archival copy also. The Authors grant you a license for re-use within non-commercial, non-profit software provided prominent credit is given and the Authors' rights are preserved. Any other uses, including, without limitation, allowing the code or its output to be accessed, used, or available to others, are not permitted.

2. 2. WARRANTY.

3. (a) The Authors and Publisher provide no warranties of any kind, either express or implied, including, without limiting the generality of the foregoing, any implied warranty of merchantability or fitness for a particular purpose.

4. (b) Neither the Authors nor Publisher shall be liable to you or any third parties for damages of any kind, including without limitation, any lost profits, lost savings, or other incidental or consequential damages arising out of, or related to, the use, inability to use, or accuracy of calculations of the code and functions contained herein, or the breach of any express or implied warranty, even ifthe Authors or Publisher have been advised of the possibility of those damages.

5. […]

This appendix contains the complete Common Lisp implementation of the calendar functions described in the text. The functions in the text were automatically typeset from the definitions in this appendix. These functions are available over the World Wide Web at

http://www.cambridge.org/us/9780521702386

Please bear in mind the limits of the License and that the copyright on this book includes the code. Also please keep in mind that if the result of any calculation is critical, it should be verified by independent means.

For licensing information about nonpersonal and other uses, contact the authors. The code is distributed in the hope that it may be useful but without any warranty as to the accuracy of its output and with liability limited to return of the price of this book, which restrictions are set forth on page xxviii.

Lisp Preliminaries

For readers unfamiliar with Lisp, this section provides the bare necessities. A complete description can be found in [1].

All functions in Lisp are written in prefix notation. If f is a defined function, then applies f to the n + 1 arguments e0, e1, e2, … en.

The following description of the presentation of the annual calendar in China is taken from Peter (Pierre) Hoang (A Notice of the Chinese Calendar and a Concordance with the European Calendar, 2nd ed., Catholic Mission Press, Shanghai, 1904):

The International Organization for Standardization (ISO) calendar, popular in Sweden and other European countries, specifies a date by giving the ordinal day in the week and the “calendar week” in a Gregorian year. The ISO standard [1, sec. 2.2.10] defines the calendar week number as the

This does not define a new calendar per se, but rather a representation of dates on the Gregorian calendar; still, it is convenient for us to treat it as a separate calendar because the representation depends on weeks and the day of the week.

It follows from the ISO standard that an ISO year begins with the Monday between December 29 and January 4 and ends with a Sunday between December 28 and January 3. Accordingly, a year on the ISO calendar consists of 52 or 53 whole weeks, making the year either 364 or 371 days long. The epoch is the same as the Gregorian calendar, namely R.D. 1, because January 1, 1 (Gregorian) was a Monday.

This book has developed over a 20-year period during which the calendrical algorithms and our presentation of them have continually evolved. Our initial motivation wasaneffort by one of us (E.M.R.) to create Emacs-Lisp code that would provide calendar and diary features for GNU Emacs [8]; this version of the code included the Gregorian, Islamic, and Hebrew calendars (the Hebrew implemented by N.D.). A deluge of inquiries from around the globe soon made it clear to us that there was keen interest in an explanation that would go beyond the code itself, leading to our article [2] and encouraging us to rewrite the code completely, this time in Common Lisp [9]. The subsequent addition—by popular demand—of the Mayan and French Revolutionary calendars to GNU Emacs prompted a second article [6]. We received many hundreds of reprint requests for these articles. This response far exceeded our expectations and provided the impetus to write a book in which we could more fully address the multifaceted subject of calendars and their implementation.

The subject of calendars has always fascinated us with its cultural, historical, and mathematical wealth, and we have occasionally employed calendars as accessible examples in introductory programming courses.

The Pawukon calendar of Bali is a complex example of a calendar based on concurrent cycles (see Section 1.11). The whole calendar repeats every 210 days, but these 210-day “years” are unnumbered. The calendar comprises 10 subcycles of lengths 1 through 10, all running simultaneously. The subcycles that determine the calendar are those of length 5, 6, 7; the others are altered to fit, by repetitions or other complications.

Like many other cultures in the region, the Balinese also have a lunisolar calendar of the old Hindu style (see Chapter 9), but leap months have been added erratically; we do not describe its details. This lunisolar calendar is used to determine only one holiday: Nyepi, a “New Year's Day” marking the start of the tenth lunar month, near the onset of spring.

Structure and Implementation

The main subcycles of the Pawukon calendar are those of length 5, 6, and 7, and the whole calendar repeats every 210 days, the least common multiple of 5, 6, and 7.

The Mayans, developers of an ancient Amerindian civilization in Central America, employed three separate, overlapping calendrical systems called by scholars the long count, the haab, and the tzolkin. Their civilization reached its zenith during the period 250–900 C.E., and the Mayans survive to this day in Guatemala and in the Yucatan peninsula of Mexico and Belize; some groups have preserved parts of the calendar systems.

Structure and History

The Hindus have both solar and lunisolar calendars. In the Hindu lunisolar system, as in other lunisolar calendars, months follow the lunar cycle and are synchronized with the solar year by introducing occasional leap months. Unlike the Hebrew lunisolar calendar (described in Chapter 7), Hindu intercalated months do not follow a short cyclical pattern. Moreover, unlike other calendars, a day can be omitted any time in a lunar month.

Modern Hindu calendars are based on close approximations to the true times of the sun's entrance into the signs of the zodiac and of lunar conjunctions (new moons). Before about 1100 C.E., however, Hindu calendars used mean times. Though the basic structure of the calendar is similar for both systems, the mean (madhyama) and true (spaṣṭa) calendars can differ by a few days or can be shifted by a month. In this chapter we implement the mean system, as described in [4, pp. 360–446], which is arithmetical; Chapter 18 is devoted to the more recent astronomical version. For an ancient description of Hindu astronomy, calendars, and holidays, see the book on India by al-Bīrūnā[1]; a more modern reference is [3].