// Licensed to the .NET Foundation under one or more agreements. // The .NET Foundation licenses this file to you under the MIT license. // See the LICENSE file in the project root for more information. using System.Diagnostics; namespace System.Globalization { internal class CalendricalCalculationsHelper { private const double FullCircleOfArc = 360.0; // 360.0; private const int HalfCircleOfArc = 180; private const double TwelveHours = 0.5; // half a day private const double Noon2000Jan01 = 730120.5; internal const double MeanTropicalYearInDays = 365.242189; private const double MeanSpeedOfSun = MeanTropicalYearInDays / FullCircleOfArc; private const double LongitudeSpring = 0.0; private const double TwoDegreesAfterSpring = 2.0; private const int SecondsPerDay = 24 * 60 * 60; // 24 hours * 60 minutes * 60 seconds private const int DaysInUniformLengthCentury = 36525; private const int SecondsPerMinute = 60; private const int MinutesPerDegree = 60; private static readonly long StartOf1810 = GetNumberOfDays(new DateTime(1810, 1, 1)); private static readonly long StartOf1900Century = GetNumberOfDays(new DateTime(1900, 1, 1)); private static readonly double[] s_coefficients1900to1987 = new double[] { -0.00002, 0.000297, 0.025184, -0.181133, 0.553040, -0.861938, 0.677066, -0.212591 }; private static readonly double[] s_coefficients1800to1899 = new double[] { -0.000009, 0.003844, 0.083563, 0.865736, 4.867575, 15.845535, 31.332267, 38.291999, 28.316289, 11.636204, 2.043794 }; private static readonly double[] s_coefficients1700to1799 = new double[] { 8.118780842, -0.005092142, 0.003336121, -0.0000266484 }; private static readonly double[] s_coefficients1620to1699 = new double[] { 196.58333, -4.0675, 0.0219167 }; private static readonly double[] s_lambdaCoefficients = new double[] { 280.46645, 36000.76983, 0.0003032 }; private static readonly double[] s_anomalyCoefficients = new double[] { 357.52910, 35999.05030, -0.0001559, -0.00000048 }; private static readonly double[] s_eccentricityCoefficients = new double[] { 0.016708617, -0.000042037, -0.0000001236 }; private static readonly double[] s_coefficients = new double[] { Angle(23, 26, 21.448), Angle(0, 0, -46.8150), Angle(0, 0, -0.00059), Angle(0, 0, 0.001813) }; private static readonly double[] s_coefficientsA = new double[] { 124.90, -1934.134, 0.002063 }; private static readonly double[] s_coefficientsB = new double[] { 201.11, 72001.5377, 0.00057 }; private static double RadiansFromDegrees(double degree) { return degree * Math.PI / 180; } private static double SinOfDegree(double degree) { return Math.Sin(RadiansFromDegrees(degree)); } private static double CosOfDegree(double degree) { return Math.Cos(RadiansFromDegrees(degree)); } private static double TanOfDegree(double degree) { return Math.Tan(RadiansFromDegrees(degree)); } public static double Angle(int degrees, int minutes, double seconds) { return ((seconds / SecondsPerMinute + minutes) / MinutesPerDegree) + degrees; } private static double Obliquity(double julianCenturies) { return PolynomialSum(s_coefficients, julianCenturies); } internal static long GetNumberOfDays(DateTime date) { return date.Ticks / GregorianCalendar.TicksPerDay; } private static int GetGregorianYear(double numberOfDays) { return new DateTime(Math.Min((long)(Math.Floor(numberOfDays) * GregorianCalendar.TicksPerDay), DateTime.MaxValue.Ticks)).Year; } private enum CorrectionAlgorithm { Default, Year1988to2019, Year1900to1987, Year1800to1899, Year1700to1799, Year1620to1699 } private struct EphemerisCorrectionAlgorithmMap { public EphemerisCorrectionAlgorithmMap(int year, CorrectionAlgorithm algorithm) { _lowestYear = year; _algorithm = algorithm; } internal int _lowestYear; internal CorrectionAlgorithm _algorithm; }; private static readonly EphemerisCorrectionAlgorithmMap[] s_ephemerisCorrectionTable = new EphemerisCorrectionAlgorithmMap[] { // lowest year that starts algorithm, algorithm to use new EphemerisCorrectionAlgorithmMap(2020, CorrectionAlgorithm.Default), new EphemerisCorrectionAlgorithmMap(1988, CorrectionAlgorithm.Year1988to2019), new EphemerisCorrectionAlgorithmMap(1900, CorrectionAlgorithm.Year1900to1987), new EphemerisCorrectionAlgorithmMap(1800, CorrectionAlgorithm.Year1800to1899), new EphemerisCorrectionAlgorithmMap(1700, CorrectionAlgorithm.Year1700to1799), new EphemerisCorrectionAlgorithmMap(1620, CorrectionAlgorithm.Year1620to1699), new EphemerisCorrectionAlgorithmMap(int.MinValue, CorrectionAlgorithm.Default) // default must be last }; private static double Reminder(double divisor, double dividend) { double whole = Math.Floor(divisor / dividend); return divisor - (dividend * whole); } private static double NormalizeLongitude(double longitude) { longitude = Reminder(longitude, FullCircleOfArc); if (longitude < 0) { longitude += FullCircleOfArc; } return longitude; } public static double AsDayFraction(double longitude) { return longitude / FullCircleOfArc; } private static double PolynomialSum(double[] coefficients, double indeterminate) { double sum = coefficients[0]; double indeterminateRaised = 1; for (int i = 1; i < coefficients.Length; i++) { indeterminateRaised *= indeterminate; sum += (coefficients[i] * indeterminateRaised); } return sum; } private static double CenturiesFrom1900(int gregorianYear) { long july1stOfYear = GetNumberOfDays(new DateTime(gregorianYear, 7, 1)); return (double)(july1stOfYear - StartOf1900Century) / DaysInUniformLengthCentury; } // the following formulas defines a polynomial function which gives us the amount that the earth is slowing down for specific year ranges private static double DefaultEphemerisCorrection(int gregorianYear) { Debug.Assert(gregorianYear < 1620 || 2020 <= gregorianYear); long january1stOfYear = GetNumberOfDays(new DateTime(gregorianYear, 1, 1)); double daysSinceStartOf1810 = january1stOfYear - StartOf1810; double x = TwelveHours + daysSinceStartOf1810; return ((Math.Pow(x, 2) / 41048480) - 15) / SecondsPerDay; } private static double EphemerisCorrection1988to2019(int gregorianYear) { Debug.Assert(1988 <= gregorianYear && gregorianYear <= 2019); return (double)(gregorianYear - 1933) / SecondsPerDay; } private static double EphemerisCorrection1900to1987(int gregorianYear) { Debug.Assert(1900 <= gregorianYear && gregorianYear <= 1987); double centuriesFrom1900 = CenturiesFrom1900(gregorianYear); return PolynomialSum(s_coefficients1900to1987, centuriesFrom1900); } private static double EphemerisCorrection1800to1899(int gregorianYear) { Debug.Assert(1800 <= gregorianYear && gregorianYear <= 1899); double centuriesFrom1900 = CenturiesFrom1900(gregorianYear); return PolynomialSum(s_coefficients1800to1899, centuriesFrom1900); } private static double EphemerisCorrection1700to1799(int gregorianYear) { Debug.Assert(1700 <= gregorianYear && gregorianYear <= 1799); double yearsSince1700 = gregorianYear - 1700; return PolynomialSum(s_coefficients1700to1799, yearsSince1700) / SecondsPerDay; } private static double EphemerisCorrection1620to1699(int gregorianYear) { Debug.Assert(1620 <= gregorianYear && gregorianYear <= 1699); double yearsSince1600 = gregorianYear - 1600; return PolynomialSum(s_coefficients1620to1699, yearsSince1600) / SecondsPerDay; } // ephemeris-correction: correction to account for the slowing down of the rotation of the earth private static double EphemerisCorrection(double time) { int year = GetGregorianYear(time); foreach (EphemerisCorrectionAlgorithmMap map in s_ephemerisCorrectionTable) { if (map._lowestYear <= year) { switch (map._algorithm) { case CorrectionAlgorithm.Default: return DefaultEphemerisCorrection(year); case CorrectionAlgorithm.Year1988to2019: return EphemerisCorrection1988to2019(year); case CorrectionAlgorithm.Year1900to1987: return EphemerisCorrection1900to1987(year); case CorrectionAlgorithm.Year1800to1899: return EphemerisCorrection1800to1899(year); case CorrectionAlgorithm.Year1700to1799: return EphemerisCorrection1700to1799(year); case CorrectionAlgorithm.Year1620to1699: return EphemerisCorrection1620to1699(year); } break; // break the loop and assert eventually } } Debug.Assert(false, "Not expected to come here"); return DefaultEphemerisCorrection(year); } public static double JulianCenturies(double moment) { double dynamicalMoment = moment + EphemerisCorrection(moment); return (dynamicalMoment - Noon2000Jan01) / DaysInUniformLengthCentury; } private static bool IsNegative(double value) { return Math.Sign(value) == -1; } private static double CopySign(double value, double sign) { return (IsNegative(value) == IsNegative(sign)) ? value : -value; } // equation-of-time; approximate the difference between apparent solar time and mean solar time // formal definition is EOT = GHA - GMHA // GHA is the Greenwich Hour Angle of the apparent (actual) Sun // GMHA is the Greenwich Mean Hour Angle of the mean (fictitious) Sun // http://www.esrl.noaa.gov/gmd/grad/solcalc/ // http://en.wikipedia.org/wiki/Equation_of_time private static double EquationOfTime(double time) { double julianCenturies = JulianCenturies(time); double lambda = PolynomialSum(s_lambdaCoefficients, julianCenturies); double anomaly = PolynomialSum(s_anomalyCoefficients, julianCenturies); double eccentricity = PolynomialSum(s_eccentricityCoefficients, julianCenturies); double epsilon = Obliquity(julianCenturies); double tanHalfEpsilon = TanOfDegree(epsilon / 2); double y = tanHalfEpsilon * tanHalfEpsilon; double dividend = ((y * SinOfDegree(2 * lambda)) - (2 * eccentricity * SinOfDegree(anomaly)) + (4 * eccentricity * y * SinOfDegree(anomaly) * CosOfDegree(2 * lambda)) - (0.5 * Math.Pow(y, 2) * SinOfDegree(4 * lambda)) - (1.25 * Math.Pow(eccentricity, 2) * SinOfDegree(2 * anomaly))); double divisor = 2 * Math.PI; double equation = dividend / divisor; // approximation of equation of time is not valid for dates that are many millennia in the past or future // thus limited to a half day return CopySign(Math.Min(Math.Abs(equation), TwelveHours), equation); } private static double AsLocalTime(double apparentMidday, double longitude) { // slightly inaccurate since equation of time takes mean time not apparent time as its argument, but the difference is negligible double universalTime = apparentMidday - AsDayFraction(longitude); return apparentMidday - EquationOfTime(universalTime); } // midday public static double Midday(double date, double longitude) { return AsLocalTime(date + TwelveHours, longitude) - AsDayFraction(longitude); } private static double InitLongitude(double longitude) { return NormalizeLongitude(longitude + HalfCircleOfArc) - HalfCircleOfArc; } // midday-in-tehran public static double MiddayAtPersianObservationSite(double date) { return Midday(date, InitLongitude(52.5)); // 52.5 degrees east - longitude of UTC+3:30 which defines Iranian Standard Time } private static double PeriodicTerm(double julianCenturies, int x, double y, double z) { return x * SinOfDegree(y + z * julianCenturies); } private static double SumLongSequenceOfPeriodicTerms(double julianCenturies) { double sum = 0.0; sum += PeriodicTerm(julianCenturies, 403406, 270.54861, 0.9287892); sum += PeriodicTerm(julianCenturies, 195207, 340.19128, 35999.1376958); sum += PeriodicTerm(julianCenturies, 119433, 63.91854, 35999.4089666); sum += PeriodicTerm(julianCenturies, 112392, 331.2622, 35998.7287385); sum += PeriodicTerm(julianCenturies, 3891, 317.843, 71998.20261); sum += PeriodicTerm(julianCenturies, 2819, 86.631, 71998.4403); sum += PeriodicTerm(julianCenturies, 1721, 240.052, 36000.35726); sum += PeriodicTerm(julianCenturies, 660, 310.26, 71997.4812); sum += PeriodicTerm(julianCenturies, 350, 247.23, 32964.4678); sum += PeriodicTerm(julianCenturies, 334, 260.87, -19.441); sum += PeriodicTerm(julianCenturies, 314, 297.82, 445267.1117); sum += PeriodicTerm(julianCenturies, 268, 343.14, 45036.884); sum += PeriodicTerm(julianCenturies, 242, 166.79, 3.1008); sum += PeriodicTerm(julianCenturies, 234, 81.53, 22518.4434); sum += PeriodicTerm(julianCenturies, 158, 3.5, -19.9739); sum += PeriodicTerm(julianCenturies, 132, 132.75, 65928.9345); sum += PeriodicTerm(julianCenturies, 129, 182.95, 9038.0293); sum += PeriodicTerm(julianCenturies, 114, 162.03, 3034.7684); sum += PeriodicTerm(julianCenturies, 99, 29.8, 33718.148); sum += PeriodicTerm(julianCenturies, 93, 266.4, 3034.448); sum += PeriodicTerm(julianCenturies, 86, 249.2, -2280.773); sum += PeriodicTerm(julianCenturies, 78, 157.6, 29929.992); sum += PeriodicTerm(julianCenturies, 72, 257.8, 31556.493); sum += PeriodicTerm(julianCenturies, 68, 185.1, 149.588); sum += PeriodicTerm(julianCenturies, 64, 69.9, 9037.75); sum += PeriodicTerm(julianCenturies, 46, 8.0, 107997.405); sum += PeriodicTerm(julianCenturies, 38, 197.1, -4444.176); sum += PeriodicTerm(julianCenturies, 37, 250.4, 151.771); sum += PeriodicTerm(julianCenturies, 32, 65.3, 67555.316); sum += PeriodicTerm(julianCenturies, 29, 162.7, 31556.08); sum += PeriodicTerm(julianCenturies, 28, 341.5, -4561.54); sum += PeriodicTerm(julianCenturies, 27, 291.6, 107996.706); sum += PeriodicTerm(julianCenturies, 27, 98.5, 1221.655); sum += PeriodicTerm(julianCenturies, 25, 146.7, 62894.167); sum += PeriodicTerm(julianCenturies, 24, 110.0, 31437.369); sum += PeriodicTerm(julianCenturies, 21, 5.2, 14578.298); sum += PeriodicTerm(julianCenturies, 21, 342.6, -31931.757); sum += PeriodicTerm(julianCenturies, 20, 230.9, 34777.243); sum += PeriodicTerm(julianCenturies, 18, 256.1, 1221.999); sum += PeriodicTerm(julianCenturies, 17, 45.3, 62894.511); sum += PeriodicTerm(julianCenturies, 14, 242.9, -4442.039); sum += PeriodicTerm(julianCenturies, 13, 115.2, 107997.909); sum += PeriodicTerm(julianCenturies, 13, 151.8, 119.066); sum += PeriodicTerm(julianCenturies, 13, 285.3, 16859.071); sum += PeriodicTerm(julianCenturies, 12, 53.3, -4.578); sum += PeriodicTerm(julianCenturies, 10, 126.6, 26895.292); sum += PeriodicTerm(julianCenturies, 10, 205.7, -39.127); sum += PeriodicTerm(julianCenturies, 10, 85.9, 12297.536); sum += PeriodicTerm(julianCenturies, 10, 146.1, 90073.778); return sum; } private static double Aberration(double julianCenturies) { return (0.0000974 * CosOfDegree(177.63 + (35999.01848 * julianCenturies))) - 0.005575; } private static double Nutation(double julianCenturies) { double a = PolynomialSum(s_coefficientsA, julianCenturies); double b = PolynomialSum(s_coefficientsB, julianCenturies); return (-0.004778 * SinOfDegree(a)) - (0.0003667 * SinOfDegree(b)); } public static double Compute(double time) { double julianCenturies = JulianCenturies(time); double lambda = 282.7771834 + (36000.76953744 * julianCenturies) + (0.000005729577951308232 * SumLongSequenceOfPeriodicTerms(julianCenturies)); double longitude = lambda + Aberration(julianCenturies) + Nutation(julianCenturies); return InitLongitude(longitude); } public static double AsSeason(double longitude) { return (longitude < 0) ? (longitude + FullCircleOfArc) : longitude; } private static double EstimatePrior(double longitude, double time) { double timeSunLastAtLongitude = time - (MeanSpeedOfSun * AsSeason(InitLongitude(Compute(time) - longitude))); double longitudeErrorDelta = InitLongitude(Compute(timeSunLastAtLongitude) - longitude); return Math.Min(time, timeSunLastAtLongitude - (MeanSpeedOfSun * longitudeErrorDelta)); } // persian-new-year-on-or-before // number of days is the absolute date. The absolute date is the number of days from January 1st, 1 A.D. // 1/1/0001 is absolute date 1. internal static long PersianNewYearOnOrBefore(long numberOfDays) { double date = (double)numberOfDays; double approx = EstimatePrior(LongitudeSpring, MiddayAtPersianObservationSite(date)); long lowerBoundNewYearDay = (long)Math.Floor(approx) - 1; long upperBoundNewYearDay = lowerBoundNewYearDay + 3; // estimate is generally within a day of the actual occurrance (at the limits, the error expands, since the calculations rely on the mean tropical year which changes...) long day = lowerBoundNewYearDay; for (; day != upperBoundNewYearDay; ++day) { double midday = MiddayAtPersianObservationSite((double)day); double l = Compute(midday); if ((LongitudeSpring <= l) && (l <= TwoDegreesAfterSpring)) { break; } } Debug.Assert(day != upperBoundNewYearDay); return day - 1; } } }