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Provides date of easter and other calendar related arithmetic.

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Wolfgang Helbig 1997-12-04 10:41:49 +00:00
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# $Id$
LIB= calendar
SRCS= calendar.c easter.c
MAN3= calendar.3
MLINKS= calendar.3 easterg.3 calendar.3 easterj.3 \
calendar.3 gdate.3 calendar.3 jdate.3 \
calendar.3 ndaysg.3 calendar.3 ndaysj.3 \
calendar.3 week.3 calendar.3 weekday.3
CFLAGS+=-I. -I${.CURDIR} -Wall
beforeinstall:
${INSTALL} -C -m 444 -o $(BINOWN) -g $(BINGRP) ${.CURDIR}/calendar.h \
${DESTDIR}/usr/include
.include <bsd.lib.mk>

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.\" Copyright (c) 1997 Wolfgang Helbig
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" $Id$
.\"
.Dd November 29, 1997
.Dt CALENDAR 3
.Os
.Sh NAME
.Nm easterg ,
.Nm easterj ,
.Nm gdate ,
.Nm jdate ,
.Nm ndaysg ,
.Nm ndaysj ,
.Nm week ,
.Nm weekday
.Nd Calendar arithmetic for the Christian era.
.Sh SYNOPSIS
.Fd #include <calendar.h>
.Ft date *
.Fn easterg "int year" "date *dt"
.Ft date *
.Fn easterj "int year" "date *dt"
.Ft date *
.Fn gdate "int nd" "date *dt"
.Ft date *
.Fn jdate "int nd" "date *dt"
.Ft int
.Fn ndaysg "date *dt"
.Ft int
.Fn ndaysj "date *dt"
.Ft int
.Fn week "int nd" "int *year"
.Ft int
.Fn weekday "int nd"
.Sh DESCRIPTION
These functions provide calendar arithmetic for a large range of years,
starting at March 1st, year zero (i. e. 1 B.C.) and ending way beyond
year 100000.
Programs should be linked with
.Fl lcalendar .
The functions
.Fn easterg
and
.Fn easterj
store the date of Easter Sunday into the structure pointed at by
.Fa dt
and return a pointer to this structure.
The function
.Fn easterg
assumes Gregorian Calendar (adopted by most western churches after 1582) and
.Fn easterj
assumes Julian Calendar (Western churches before 1582 and Greek Church
until today).
The functions
.Fn gdate ,
.Fn jdate ,
.Fn ndaysg
and
.Fn ndaysj
provide conversions between the common "year, month, day" notation
of a date and the "number of days" representation, which is better suited
for calculations. The days are numbered from March 1st year 1 B.C., starting
with zero, so the number of a day gives the number of days since March 1st,
year 1 B.C. The conversions work for nonnegative day numbers only.
The
.Fn gdate
and
.Fn jdate
functions
store the date corresponding to the day number
.Fa nd
into the structure pointed at by
.Fa dt
and return a pointer to this structure.
The
.Fn ndaysg
and
.Fn ndaysj
functions
return the day number of the date pointed at by
.Fa dt .
The
.Fn gdate
and
.Fn ndaysg
functions
assume Gregorian Calendar after October 4th 1582 and Julian Calendar before,
whereas
.Fn jdate
and
.Fn ndaysj
assume Julian Calendar throughout.
The two calendars differ by the definition of the leap year. The
Julian Calendar says every year that is a multiple of four is a
leap year. The Gregorian Calendar excludes years that are multiples of
100 and not multiples of 400.
This means the years 1700, 1800, 1900, 2100 are not leap years
and the year 2000 is
a leap year.
The new rules were inaugurated on October 4th 1582 by deleting ten
days following this date.
The function
.Fn week
returns the number of the week which contains the day numbered
.Fa nd .
The argument
.Fa *year
is set with the year that contains (the greater part of) the week.
The weeks are numbered per year starting with week 1, which is the
first week in a year that includes more than three days of the year.
Weeks start on Monday.
This function is defined for Gregorian Calendar only.
The function
.Fn weekday
returns the weekday (Mo = 0 .. Su = 6) of the day numbered
.Fa nd .
The type
.Fa date
is a structure defined in
.Aq Pa calendar.h .
It contains these fields:
.Bd -literal -offset indent
int y; /\(** year (0000 - ????) \(**/
int m; /\(** month (1 - 12) \(**/
int d; /\(** day of month (1 - 31) \(**/
.Ed
The year zero is written as "1 B.C." by historians and "0" by astronomers
and in this library.
.Sh SEE ALSO
.Xr ncal 1 ,
.Xr strftime 3
.Rs
.%A A. B. Author
.%D November 1997
.Sh STANDARDS
The week number conforms to ISO 8601: 1988.
.Sh HISTORY
The
.Nm calendar
library first appeared in
.Fx 3.0 .
.Sh AUTHOR
This manual page and the library was written by
.An Wolfgang Helbig Aq helbig@FreeBSD.ORG .
.Sh BUGS
The library was coded with great care so there are no bugs left.

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/*-
* Copyright (c) 1997 Wolfgang Helbig
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* $Id$
*/
#include "calendar.h"
#ifndef NULL
#define NULL 0
#endif
/*
* For each month tabulate the number of days elapsed in a year before the
* month. This assumes the internal date representation, where a year
* starts on March 1st. So we don't need a special table for leap years.
* But we do need a special table for the year 1582, since 10 days are
* deleted in October. This is month1s for the switch from Julian to
* Gregorian calendar.
*/
static int const month1[] =
{0, 31, 61, 92, 122, 153, 184, 214, 245, 275, 306, 337};
/* M A M J J A S O N D J */
static int const month1s[]=
{0, 31, 61, 92, 122, 153, 184, 214, 235, 265, 296, 327};
/* The last day of Julian calendar, in internal and ndays representation */
static int nswitch; /* The last day of Julian calendar */
static date jiswitch = {1582, 7, 3};
static date *date2idt(date *idt, date *dt);
static date *idt2date(date *dt, date *idt);
static int ndaysji(date *idt);
static int ndaysgi(date *idt);
static int firstweek(int year);
/*
* Compute the Julian date from the number of days elapsed since
* March 1st of year zero.
*/
date *
jdate(int ndays, date *dt)
{
date idt; /* Internal date representation */
int r; /* hold the rest of days */
/*
* Compute the year by starting with an approximation not smaller
* than the answer and using linear search for the greatest
* year which does not begin after ndays.
*/
idt.y = ndays / 365;
idt.m = 0;
idt.d = 0;
while ((r = ndaysji(&idt)) > ndays)
idt.y--;
/*
* Set r to the days left in the year and compute the month by
* linear search as the largest month that does not begin after r
* days.
*/
r = ndays - r;
for (idt.m = 11; month1[idt.m] > r; idt.m--)
;
/* Compute the days left in the month */
idt.d = r - month1[idt.m];
/* return external representation of the date */
return (idt2date(dt, &idt));
}
/*
* Return the number of days since March 1st of the year zero.
* The date is given according to Julian calendar.
*/
int
ndaysj(date *dt)
{
date idt; /* Internal date representation */
if (date2idt(&idt, dt) == NULL)
return (-1);
else
return (ndaysji(&idt));
}
/*
* Same as above, where the Julian date is given in internal notation.
* This formula shows the beauty of this notation.
*/
static int
ndaysji(date * idt)
{
return (idt->d + month1[idt->m] + idt->y * 365 + idt->y / 4);
}
/*
* Compute the date according to the Gregorian calendar from the number of
* days since March 1st, year zero. The date computed will be Julian if it
* is older than 1582-10-05. This is the reverse of the function ndaysg().
*/
date *
gdate(int ndays, date *dt)
{
int const *montht; /* month-table */
date idt; /* for internal date representation */
int r; /* holds the rest of days */
/*
* Compute the year by starting with an approximation not smaller
* than the answer and search linearly for the greatest year not
* starting after ndays.
*/
idt.y = ndays / 365;
idt.m = 0;
idt.d = 0;
while ((r = ndaysgi(&idt)) > ndays)
idt.y--;
/*
* Set ndays to the number of days left and compute by linear
* search the greatest month which does not start after ndays. We
* use the table month1 which provides for each month the number
* of days that elapsed in the year before that month. Here the
* year 1582 is special, as 10 days are left out in October to
* resynchronize the calendar with the earth's orbit. October 4th
* 1582 is followed by October 15th 1582. We use the "switch"
* table month1s for this year.
*/
ndays = ndays - r;
if (idt.y == 1582)
montht = month1s;
else
montht = month1;
for (idt.m = 11; montht[idt.m] > ndays; idt.m--)
;
idt.d = ndays - montht[idt.m]; /* the rest is the day in month */
/* Advance ten days deleted from October if after switch in Oct 1582 */
if (idt.y == jiswitch.y && idt.m == jiswitch.m && jiswitch.d < idt.d)
idt.d += 10;
/* return external representation of found date */
return (idt2date(dt, &idt));
}
/*
* Return the number of days since March 1st of the year zero. The date is
* assumed Gregorian if younger than 1582-10-04 and Julian otherwise. This
* is the reverse of gdate.
*/
int
ndaysg(date *dt)
{
date idt; /* Internal date representation */
if (date2idt(&idt, dt) == NULL)
return (-1);
return (ndaysgi(&idt));
}
/*
* Same as above, but with the Gregorian date given in internal
* representation.
*/
static int
ndaysgi(date *idt)
{
int nd; /* Number of days--return value */
/* Cache nswitch if not already done */
if (nswitch == 0)
nswitch = ndaysji(&jiswitch);
/*
* Assume Julian calendar and adapt to Gregorian if necessary, i. e.
* younger than nswitch. Gregori deleted
* the ten days from Oct 5th to Oct 14th 1582.
* Thereafter years which are multiples of 100 and not multiples
* of 400 were not leap years anymore.
* This makes the average length of a year
* 365d +.25d - .01d + .0025d = 365.2425d. But the tropical
* year measures 365.2422d. So in 10000/3 years we are
* again one day ahead of the earth. Sigh :-)
* (d is the average length of a day and tropical year is the
* time from one spring point to the next.)
*/
if ((nd = ndaysji(idt)) == -1)
return (-1);
if (idt->y >= 1600)
nd = (nd - 10 - (idt->y - 1600) / 100 + (idt->y - 1600) / 400);
else if (nd > nswitch)
nd -= 10;
return (nd);
}
/*
* Compute the week number from the number of days since March 1st year 0.
* The weeks are numbered per year starting with 1. If the first
* week of a year includes at least four days of that year it is week 1,
* otherwise it gets the number of the last week of the previous year.
* The variable y will be filled with the year that contains the greater
* part of the week.
*/
int
week(int nd, int *y)
{
date dt;
int fw; /* 1st day of week 1 of previous, this and
* next year */
gdate(nd, &dt);
for (*y = dt.y + 1; nd < (fw = firstweek(*y)); (*y)--)
;
return ((nd - fw) / 7 + 1);
}
/* return the first day of week 1 of year y */
static int
firstweek(int y)
{
date idt;
int nd, wd;
idt.y = y - 1; /* internal representation of y-1-1 */
idt.m = 10;
idt.d = 0;
nd = ndaysgi(&idt);
/*
* If more than 3 days of this week are in the preceding year, the
* next week is week 1 (and the next monday is the answer),
* otherwise this week is week 1 and the last monday is the
* answer.
*/
if ((wd = weekday(nd)) > 3)
return (nd - wd + 7);
else
return (nd - wd);
}
/* return the weekday (Mo = 0 .. Su = 6) */
int
weekday(int nd)
{
date dmondaygi = {1997, 8, 16}; /* Internal repr. of 1997-11-17 */
static int nmonday; /* ... which is a monday */
/* Cache the daynumber of one monday */
if (nmonday == 0)
nmonday = ndaysgi(&dmondaygi);
/* return (nd - nmonday) modulo 7 which is the weekday */
nd = (nd - nmonday) % 7;
if (nd < 0)
return (nd + 7);
else
return (nd);
}
/*
* Convert a date to internal date representation: The year starts on
* March 1st, month and day numbering start at zero. E. g. March 1st of
* year zero is written as y=0, m=0, d=0.
*/
static date *
date2idt(date *idt, date *dt)
{
idt->d = dt->d - 1;
if (dt->m > 2) {
idt->m = dt->m - 3;
idt->y = dt->y;
} else {
idt->m = dt->m + 9;
idt->y = dt->y - 1;
}
if (idt->m < 0 || idt->m > 11 || idt->y < 0)
return (NULL);
else
return idt;
}
/* Reverse of date2idt */
static date *
idt2date(date *dt, date *idt)
{
dt->d = idt->d + 1;
if (idt->m < 10) {
dt->m = idt->m + 3;
dt->y = idt->y;
} else {
dt->m = idt->m - 9;
dt->y = idt->y + 1;
}
if (dt->m < 1)
return (NULL);
else
return (dt);
}

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/*-
* Copyright (c) 1997 Wolfgang Helbig
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* $Id$
*/
typedef struct date {
int y; /* year */
int m; /* month */
int d; /* day */
} date;
date *easterg(int _year, date *_dt);
date *easterj(int _year, date *_dt);
date *gdate(int _nd, date *_dt);
date *jdate(int _nd, date *_dt);
int ndaysg(date *_dt);
int ndaysj(date *_dt);
int week(int _nd, int *_year);
int weekday(int _nd);

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/*-
* Copyright (c) 1997 Wolfgang Helbig
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* $Id$
*/
#include "calendar.h"
/* Compute Easter Sunday in Gregorian Calendar */
date *
easterg(int y, date *dt)
{
int c, i, j, k, l, n;
n = y % 19;
c = y / 100;
k = (c - 17) / 25;
i = (c - c/4 -(c-k)/3 + 19 * n + 15) % 30;
i = i -(i/28) * (1 - (i/28) * (29/(i + 1)) * ((21 - n)/11));
j = (y + y/4 + i + 2 - c + c/4) % 7;
l = i - j;
dt->m = 3 + (l + 40) / 44;
dt->d = l + 28 - 31*(dt->m / 4);
dt->y = y;
return (dt);
}
/* Compute Easter Sunday in Julian Calendar */
date *
easterj(int y, date * dt)
{
/*
* Table for the easter limits in one metonic (19-year) cycle. 21
* to 31 is in March, 1 through 18 in April. Easter is the first
* sunday after the easter limit.
*/
int mc[] = {5, 25, 13, 2, 22, 10, 30, 18, 7, 27, 15, 4,
24, 12, 1, 21, 9, 29, 17};
/* Offset from a weekday to next sunday */
int ns[] = {6, 5, 4, 3, 2, 1, 7};
int dn;
/* Assign the easter limit of y to *dt */
dt->d = mc[y % 19];
if (dt->d < 21)
dt->m = 4;
else
dt->m = 3;
dt->y = y;
/* Compute the next sunday after the easter limit */
dn = ndaysj(dt);
dn += ns[weekday(dn)];
return (jdate(dn, dt));
}