astronomia/es/jm.js

/**
 * @copyright 2013 Sonia Keys
 * @copyright 2016 commenthol
 * @license MIT
 * @module jm
 */
/**
 * JM: Chapter 9, Jewish and Moslem Calendars.
 *
 * The Jewish calendar routines are implemented as a monolithic function,
 * because computations of the various results build off of common
 * intermediate results.
 *
 * The Moslem calendar routines break down nicely into some separate functions.
 *
 * Included in these are two functions that convert between Gregorian and
 * Julian calendar days without going through Julian day (JD).  As such,
 * I suppose, these or similar routines are not in chapter 7, Julian Day.
 * Package base might also be a suitable place for these, but I'm not sure
 * they are used anywhere else in the book.  Anyway, they have the quirk
 * that they are not direct inverses:  JulianToGregorian returns the day number
 * of the day of the Gregorian year, but GregorianToJulian wants the Gregorian
 * month and day of month as input.
 */

import base from './base';
import julian from './julian';

var int = Math.trunc;

/**
 * JewishCalendar returns interesting dates and facts about a given year.
 *
 * Input is a Julian or Gregorian year.
 *
 * Outputs:
 *  A:      (int) Year number in the Jewish Calendar
 *  mP:     (int) Month number of Pesach.
 *  dP:     (int) Day number of Pesach.
 *  mNY:    (int) Month number of the Jewish new year.
 *  dNY:    (int) Day number of the Jewish new year.
 *  months: (int) Number of months in this year.
 *  days:   (int) Number of days in this year.
 */
export function JewishCalendar(y) {
  var A = y + 3760;
  var D = bigD(y);
  var mP = 3;
  var dP = D;
  if (dP > 31) {
    mP++;
    dP -= 31;
  }
  // A simplification of Meeus's rule to add 163 days.  Months of Pesach
  // are either March or April with D based off of March.  Months of New
  // year are either September or August so D+163-(days from March to
  // September == 184) = D-21 must be based off of September.
  var mNY = 9;
  var dNY = D - 21;
  if (dNY > 30) {
    mNY++;
    dNY -= 30;
  }
  var months = 12;
  switch (A % 19) {
    case 0:
    case 3:
    case 6:
    case 8:
    case 11:
    case 14:
    case 17:
      months++;
      break;
  }
  // Similarly, A simplification of Meeus's rule to take the difference
  // in calendar days from NY of one year to NY of the next.  NY is based
  // on D, so difference in D is difference in day numbers of year.  Result
  // is sum of this number and the number of days in the Western calandar
  // year.
  var y1 = y + 1;
  var lf = julian.LeapYearGregorian;
  if (y1 < 1583) {
    lf = julian.LeapYearJulian;
  }
  var days = 365;
  if (lf(y1)) {
    days++;
  }
  days += bigD(y1) - D;
  return [A, mP, dP, mNY, dNY, months, days];
}

var bigD = function bigD(y) {
  // (y int)  int
  var C = base.floorDiv(y, 100);
  // const S int
  var S = 0;
  if (y >= 1583) {
    S = int(base.floorDiv(3 * C - 5, 4));
  }
  var a = (12 * y + 12) % 19;
  var b = y % 4;
  var Q = -1.904412361576 + 1.554241796621 * a + 0.25 * b - 0.003177794022 * y + S;
  var fq = Math.floor(Q);
  var iq = int(fq);
  var j = (iq + 3 * y + 5 * b + 2 - S) % 7;
  var r = Q - fq;
  // const D int
  var D = void 0;
  if (j === 2 || j === 4 || j === 6) {
    D = iq + 23;
  } else if (j === 1 && a > 6 && r >= 0.63287037) {
    D = iq + 24;
  } else if (j === 0 && a > 11 && r >= 0.897723765) {
    D = iq + 23;
  } else {
    D = iq + 22;
  }
  return int(D);
};

/**
 * MoslemToJD converts a Moslem calendar date to a Julian Day.
 * @param {Number} y - year in moslem calendar
 * @param {Number} m - month
 * @param {Number} d - day
 * @returns {Number} jd - Julian day
 */
export function MoslemToJD(y, m, d) {
  // (y, m, d int)  (jY, jDN int)
  var N = d + base.floorDiv(295001 * (m - 1) + 9900, 10000);
  var Q = base.floorDiv(y, 30);
  var R = y % 30;
  var A = base.floorDiv(11 * R + 3, 30);
  var W = 404 * Q + 354 * R + 208 + A;
  var Q1 = base.floorDiv(W, 1461);
  var Q2 = W % 1461;
  var G = 621 + 28 * Q + 4 * Q1;
  var K = base.floorDiv(Q2 * 10000, 3652422);
  var E = base.floorDiv(3652422 * K, 10000);
  var J = Q2 - E + N - 1;
  var X = G + K;
  if (J > 366 && X % 4 === 0) {
    J -= 366;
    X++;
  } else if (J > 365 && X % 4 > 0) {
    J -= 365;
    X++;
  }
  var jd = base.floorDiv(36525 * (X - 1), 100) + 1721423 + J;
  return jd;
}

/**
 * MoslemLeapYear returns true if year y of the Moslem calendar is a leap year.
 * @param {Number} year
 * @returns {Boolean} true if leap year
 */
export function MoslemLeapYear(year) {
  // (y int)  bool
  var R = year % 30;
  return (11 * R + 3) % 30 > 18;
}

/**
 * JulianToMoslem takes a year, month, and day of the Julian calendar and returns the equivalent year, month, and day of the Moslem calendar.
 *
 * @param {Number} y - julian year
 * @param {Number} m - julian month
 * @param {Number} d - julian day
 * @returns {Array} [my, mm, md]
 */
export function JulianToMoslem(y, m, d) {
  // (y, m, d int)  (my, mm, md int)
  var W = 2;
  if (y % 4 === 0) {
    W = 1;
  }
  var N = base.floorDiv(275 * m, 9) - W * base.floorDiv(m + 9, 12) + d - 30;
  var A = int(y - 623);
  var B = base.floorDiv(A, 4);
  var C2 = function (A) {
    var C = A % 4;
    var C1 = 365.25001 * C;
    var C2 = Math.floor(C1);
    if (C1 - C2 > 0.5) {
      return int(C2) + 1;
    }
    return int(C2);
  }(A);
  var Dp = 1461 * B + 170 + C2;
  var Q = base.floorDiv(Dp, 10631);
  var R = Dp % 10631;
  var J = base.floorDiv(R, 354);
  var K = R % 354;
  var O = base.floorDiv(11 * J + 14, 30);
  var my = 30 * Q + J + 1;
  var JJ = K - O + N - 1;
  var days = 354;
  if (MoslemLeapYear(y)) {
    days++;
  }
  if (JJ > days) {
    JJ -= days;
    my++;
  }
  var mm = void 0;
  var md = void 0;
  if (JJ === 355) {
    mm = 12;
    md = 30;
  } else {
    var S = base.floorDiv((JJ - 1) * 10, 295);
    mm = 1 + S;
    md = base.floorDiv(10 * JJ - 295 * S, 10);
  }
  return { year: my, month: mm, day: md };
}

/**
 * An MMonth specifies a month of the Moslum Calendar (Muharram = 1, ...).
 *
 * Upgraded to Unicode from the spellings given by Meeus.
 * Source: http://en.wikipedia.org/wiki/Islamic_calendar.
 */
var mmonths = ['', 'Muḥarram', 'Ṣafar', 'Rabīʿ I', 'Rabīʿ II', 'Jumādā I', 'Jumādā II', 'Rajab', 'Shaʿbān', 'Ramaḍān', 'Shawwāl', 'Dhū al-Qaʿda', 'Dhū al-Ḥijja'];

/**
 * String returns the Romanization of the month ("Muḥarram", "Ṣafar", ...).
 */
export function moslemMonth(m) {
  return mmonths[m];
}

export default {
  JewishCalendar: JewishCalendar,
  MoslemToJD: MoslemToJD,
  MoslemLeapYear: MoslemLeapYear,
  JulianToMoslem: JulianToMoslem,
  moslemMonth: moslemMonth
};