'easter.cpp' : Maik Meyer and Gary Kronk pointed out that the algorit…

…hm used here is for the Gregorian calendar, and produces misleading results for years before 1583.

easter.cpp

@@ -27,19 +27,22 @@ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
       Unlike the formula given by Gauss,  this method has no exception and
    is valid for all years in the Gregorian calendar,  hence from 1583 on."
 
-   I modified the method to include negative years by taking advantage
-of the fact that,  in the Gregorian calendar,  Easter recurs on a 5.7
-million year cycle. Add 5.7 million to the year,  and all numbers are
-positive (as long as year > -5700000,  of course!  I suppose one could
-add,  say,  570 million instead,  extending the range to cover roughly
-the Paleozoic era to a time 1.5 billion years hence...)
+   Note that this formula results from the Gregorian calendar change.
+Before 1583,  different rules were used to determine the date of Easter.
+You can use the formula for dates before 1583,  but the results will
+not match the dates when Easter was actually observed.
+
+   The relevant pages from _General Astronomy_ can be found at
+
+https://archive.org/details/generalastronomy0000hspe/page/72/mode/2up
 
    The test program can be run with zero,  one,  or two command line
 arguments,  to get three very different types of output.
 
-   If run without command-line arguments,  the program computes the day
-of Easter over an entire 5.7 million year cycle.  That lets it show the
-frequency on which Easter occurs on a given day;  the result looks like
+   Easter repeats over a cycle of 5.7 million years.  If run without
+command-line arguments,  this program computes the day of Easter over an
+entire cycle.  That lets it show the frequency on which Easter occurs on
+a given day;  the result looks like
 
 Mar 22: 0.48333 = 29/60    Apr  3: 3.38333 = 203/60   Apr 15: 3.38333 = 203/60
 Mar 23: 0.95000 = 19/20    Apr  4: 3.26666 = 49/15    Apr 16: 3.26666 = 49/15
@@ -74,23 +77,20 @@ Easter for a 75-year time span.  For example,  'easter 2010' gives
 2024 Mar 31    2039 Apr 10    2054 Mar 29    2069 Apr 14    2084 Mar 26
 
    Run with two command line arguments of a month (3=March or 4=April) and
-a day,  one gets a list of years from 0 AD to 10000 AD when Easter would
+a day,  one gets a list of years from 1583 AD to 10000 AD when Easter would
 fall on that day.  For example,  'easter 3 22' would give the following
 list of years when Easter fell on 22 March,  the earliest day possible:
 
-   15  387  482  539  607  854 1074 1131 1226 1503 1598 1693 1761 1818 2285
- 2353 2437 2505 2972 3029 3401 3496 3564 3648 3716 4308 5299 5671 6043 6195
- 6263 6415 6635 6703 6798 6882 6950 7322 7474 7542 7637 7789 7914 8161 8533
- 8685 8753 8848 8905 9125 9220 9372 9440 9812 9964
-55 found over 10000 years
-*/
+ 1598 1693 1761 1818 2285 2353 2437 2505 2972 3029 3401 3496 3564 3648 3716
+ 4308 5299 5671 6043 6195 6263 6415 6635 6703 6798 6882 6950 7322 7474 7542
+ 7637 7789 7914 8161 8533 8685 8753 8848 8905 9125 9220 9372 9440 9812 9964
 
-void easter_date( const long year, int *month, int *day);
+45 found over 8417 years
+*/
 
 void easter_date( const long year, int *month, int *day)
 {
-   const long year2 = year + 5700000L;
-   const long a = year2 % 19L, b = year2 / 100L, c = year2 % 100L;
+   const long a = year % 19L, b = year / 100L, c = year % 100L;
    const long d = b / 4L, e = b % 4L, f = (b + 8L) / 25L;
    const long g = (b - f + 1L) / 3L, h = (19L * a + b - d - g + 15L) % 30L;
    const long i = c / 4L, k = c % 4L, l = (32L + e + e + i + i - h - k) % 7L;
@@ -145,7 +145,7 @@ int main( int argc, char **argv)
       {
       int n_found = 0;
 
-      for( year = 0; year < 10000; year++)
+      for( year = 1583; year < 10000; year++)
          {
          easter_date( year, &month, &day);
          if( month == atoi( argv[1]) && day == atoi( argv[2]))
@@ -155,7 +155,7 @@ int main( int argc, char **argv)
                printf( "\n");
             }
          }
-      printf( "\n%d found over 10000 years\n", n_found);
+      printf( "\n%d found over 8417 years\n", n_found);
       }
    else
       {
@@ -207,7 +207,7 @@ int main( int argc, char **argv)
       printf( "\nRun 'easter' with a year on the command line to get the date\n");
       printf( "of Easter for that year.  For example,  'easter 2008' will\n");
       printf( "get the output 'March 23'.  Alternatively,  give a month and\n");
-      printf( "day on the command line to get the years between 0 and 10000\n");
+      printf( "day on the command line to get the years between 1583 and 10000\n");
       printf( "when Easter will fall on that day.  For example,  'easter 3 23'\n");
       printf( "will produce a list of all years when Easter is on 23 March.\n");
       printf( "\nNote that Easter cannot occur before 22 March or after 25 April.\n");