moment.easter.js

'use strict';

var moment;
if (typeof require !== 'undefined') {
    moment = require('moment');
} else {
    moment = this.moment;
}

/*
 * I found this algorithm on
 * http://www.merlyn.demon.co.uk/estralgs.txt
 *
 * Given by
 * Al Petrofsky, San Mateo County, California, U.S.A., E-mail 2009-05-22
 *
 *
 * To get Month & Day in 23 total arithmetic operations, use:
 *   c = 148 - b - ((year * 5 / 4 | 0) + a - b) % 7;
 *   Month = (c / 31 | 0);
 *   Day = c % 31 + 1;
 *
 * The coefficients in the formula for A were chosen so that both of
 * these equations would hold:
 *
 *   a / 25 % 30 == ((y / 100 * 17 + 11) / 25 - y / 400 + 16) % 30
 *   a % 7 == (y / 400 + y / 100 * 6 + 2) % 7
 *
 * As a result, the formulae for B and the return value are
 * equivalent to:
 *
 * b = ( 29 * 11 * (15 + y % 19 * 19
 *                     + y / 100 - y / 400
 *                     - (   (y / 100 + 25 - 14) * 8 / 25
 *                         - (          25 - 14) * 8 / 25)
 *                     + 1)
 *       - 1 - y % 19)
 *     % (30 * 29 * 11) / (30 * 11)
 * return 28 + b - (2 + b + y + y / 4 - y / 100 + y / 400) % 7
 *
 * B represents the date of the Paschal Full Moon, ranging from 0
 * for March 21st to 28 for April 18th.
 *
 * Here are some pertinent facts about the constants in these
 * formulae:
 *
 * 400 is the number of years in the cycle of solar corrections.
 * 100 is the number of years between solar or lunar corrections.
 *  30 is the number of different epacts (not distinguishing xxv and 25).
 *  29 is the number of different Paschal Full Moon dates.
 *  28 is the day of March one week after the equinox.
 *  25 is the number of centuries in the cycle of lunar corrections.
 *  19 is the number of years in the Metonic cycle.
 *  19 is also the ordinary decrement from one year's epact to the next.
 *  15 is the number of days after the equinox that the Paschal
 *     Full Moon falls, in the year zero.
 *  14 is one hundredth of the year at the start of the first span of
 *     four centuries between lunar corrections.
 *  11 is the number of golden numbers for which epact xxv/25 maps to
 *     a Paschal Full Moon date of April 18th rather than April 17th.
 *   8 is the number of lunar corrections per 25 centuries.
 *   7 is the number of days in the week.
 *   4 is the number of years in the uncorrected leap year cycle.
 *   2 is the number of days that are after the first Sunday after the
 *     equinox, but on or before March 28, in the year zero.
 *
 * Implementation limits:
 *
 * In C and other languages and systems with ordinary fixed-width
 * 32-bit unsigned integer arithmetic, the function fails due to
 * overflow at year 58,714,311, and with 64-bit integers, it fails
 * at year 252,188,329,394,345,111.  In either case, if a "y = y %
 * 5700000" line is added at the start of the function, then correct
 * results will be returned for all possible inputs.
 *
 * In ECMAscript/javascript: the language has no integer division
 * operator, and non-integer division results must somehow be
 * rounded down.  If division results are truncated by using a
 * bitwise logical operation (e.g. "|0") to cause an internal
 * floating-point-to-integer conversion, then the first year for
 * which the function fails is 1,717,986,919, which is when (y * 5 /
 * 4) first exceeds the 31-bit range for unsigned logical integer
 * values.  If division results are truncated using the Math.floor
 * function, then first failure comes at year 123,138,832,709,500,
 * shortly after the sum in the B formula first exceeds the 53-bit
 * positive range over which IEEE 64-bit floating point values have
 * integer precision.  In either case, if a "y = y % 5700000" line
 * is added at the start of the function, then the correct result
 * will be returned for any input that is a non-negative integer.
 */

moment.easter = function Easter20ops(year) {
    /*jslint bitwise: true, vars: true */
    var a = (year / 100 | 0) * 1483 - (year / 400 | 0) * 2225 + 2613;
    var b = ((year % 19 * 3510 + (a / 25 | 0) * 319) / 330 | 0) % 29;
    var c = 148 - b - ((year * 5 / 4 | 0) + a - b) % 7;

    return moment({year: year, month: (c / 31 | 0) - 1, day: c % 31 + 1});
};

moment.fn.easter = function () {
    return moment.easter(this.year());
};

if (typeof module !== 'undefined') {
    module.exports = moment;
} else {
    this.moment = moment;
}