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authorJiyoung Yun <jy910.yun@samsung.com>2017-04-13 14:17:19 +0900
committerJiyoung Yun <jy910.yun@samsung.com>2017-04-13 14:17:19 +0900
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tree7e5d979695fc4a431740982eb1cfecc2898b23a5 /src/mscorlib/src/System/Globalization/CalendricalCalculationsHelper.cs
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Imported Upstream version 2.0.0.11353upstream/2.0.0.11353
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-// 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.
-
-namespace System.Globalization
-{
- using System;
- using System.Diagnostics;
- using System.Diagnostics.Contracts;
-
- internal class CalendricalCalculationsHelper
- {
- const double FullCircleOfArc = 360.0; // 360.0;
- const int HalfCircleOfArc = 180;
- const double TwelveHours = 0.5; // half a day
- const double Noon2000Jan01 = 730120.5;
- internal const double MeanTropicalYearInDays = 365.242189;
- const double MeanSpeedOfSun = MeanTropicalYearInDays / FullCircleOfArc;
- const double LongitudeSpring = 0.0;
- const double TwoDegreesAfterSpring = 2.0;
- const int SecondsPerDay = 24 * 60 * 60; // 24 hours * 60 minutes * 60 seconds
-
- const int DaysInUniformLengthCentury = 36525;
- const int SecondsPerMinute = 60;
- const int MinutesPerDegree = 60;
-
- static long StartOf1810 = GetNumberOfDays(new DateTime(1810, 1, 1));
- static long StartOf1900Century = GetNumberOfDays(new DateTime(1900, 1, 1));
-
- static double[] Coefficients1900to1987 = new double[] { -0.00002, 0.000297, 0.025184, -0.181133, 0.553040, -0.861938, 0.677066, -0.212591 };
- static double[] 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 };
- static double[] Coefficients1700to1799 = new double[] { 8.118780842, -0.005092142, 0.003336121, -0.0000266484 };
- static double[] Coefficients1620to1699 = new double[] { 196.58333, -4.0675, 0.0219167 };
- static double[] LambdaCoefficients = new double[] { 280.46645, 36000.76983, 0.0003032 };
- static double[] AnomalyCoefficients = new double[] { 357.52910, 35999.05030, -0.0001559, -0.00000048 };
- static double[] EccentricityCoefficients = new double[] { 0.016708617, -0.000042037, -0.0000001236 };
- static double[] Coefficients = new double[] { Angle(23, 26, 21.448), Angle(0, 0, -46.8150), Angle(0, 0, -0.00059), Angle(0, 0, 0.001813) };
- static double[] CoefficientsA = new double[] { 124.90, -1934.134, 0.002063 };
- static double[] CoefficientsB = new double[] { 201.11, 72001.5377, 0.00057 };
-
- static double RadiansFromDegrees(double degree)
- {
- return degree * Math.PI / 180;
- }
-
- static double SinOfDegree(double degree)
- {
- return Math.Sin(RadiansFromDegrees(degree));
- }
-
- static double CosOfDegree(double degree)
- {
- return Math.Cos(RadiansFromDegrees(degree));
- }
- 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;
- }
-
- static double Obliquity(double julianCenturies)
- {
- return PolynomialSum(Coefficients, julianCenturies);
- }
-
- internal static long GetNumberOfDays(DateTime date)
- {
- return date.Ticks / GregorianCalendar.TicksPerDay;
- }
-
- static int GetGregorianYear(double numberOfDays)
- {
- return new DateTime(Math.Min((long)(Math.Floor(numberOfDays) * GregorianCalendar.TicksPerDay), DateTime.MaxValue.Ticks)).Year;
- }
-
- enum CorrectionAlgorithm
- {
- Default,
- Year1988to2019,
- Year1900to1987,
- Year1800to1899,
- Year1700to1799,
- Year1620to1699
- }
-
- struct EphemerisCorrectionAlgorithmMap
- {
- public EphemerisCorrectionAlgorithmMap(int year, CorrectionAlgorithm algorithm)
- {
- _lowestYear = year;
- _algorithm = algorithm;
- }
-
- internal int _lowestYear;
- internal CorrectionAlgorithm _algorithm;
- };
-
- static EphemerisCorrectionAlgorithmMap[] 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
- };
-
- static double Reminder(double divisor, double dividend)
- {
- double whole = Math.Floor(divisor / dividend);
- return divisor - (dividend * whole);
- }
-
- static double NormalizeLongitude(double longitude)
- {
- longitude = Reminder(longitude, FullCircleOfArc);
- if (longitude < 0)
- {
- longitude += FullCircleOfArc;
- }
- return longitude;
- }
-
- static public double AsDayFraction(double longitude)
- {
- return longitude / FullCircleOfArc;
- }
-
- 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;
- }
-
- 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
- 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;
- }
-
- static double EphemerisCorrection1988to2019(int gregorianYear)
- {
- Debug.Assert(1988 <= gregorianYear && gregorianYear <= 2019);
- return (double)(gregorianYear - 1933) / SecondsPerDay;
- }
-
- static double EphemerisCorrection1900to1987(int gregorianYear)
- {
- Debug.Assert(1900 <= gregorianYear && gregorianYear <= 1987);
- double centuriesFrom1900 = CenturiesFrom1900(gregorianYear);
- return PolynomialSum(Coefficients1900to1987, centuriesFrom1900);
- }
-
- static double EphemerisCorrection1800to1899(int gregorianYear)
- {
- Debug.Assert(1800 <= gregorianYear && gregorianYear <= 1899);
- double centuriesFrom1900 = CenturiesFrom1900(gregorianYear);
- return PolynomialSum(Coefficients1800to1899, centuriesFrom1900);
- }
-
- static double EphemerisCorrection1700to1799(int gregorianYear)
- {
- Debug.Assert(1700 <= gregorianYear && gregorianYear <= 1799);
- double yearsSince1700 = gregorianYear - 1700;
- return PolynomialSum(Coefficients1700to1799, yearsSince1700) / SecondsPerDay;
- }
-
- static double EphemerisCorrection1620to1699(int gregorianYear)
- {
- Debug.Assert(1620 <= gregorianYear && gregorianYear <= 1699);
- double yearsSince1600 = gregorianYear - 1600;
- return PolynomialSum(Coefficients1620to1699, yearsSince1600) / SecondsPerDay;
- }
-
- // ephemeris-correction: correction to account for the slowing down of the rotation of the earth
- static double EphemerisCorrection(double time)
- {
- int year = GetGregorianYear(time);
- foreach (EphemerisCorrectionAlgorithmMap map in 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);
- }
-
- static public double JulianCenturies(double moment)
- {
- double dynamicalMoment = moment + EphemerisCorrection(moment);
- return (dynamicalMoment - Noon2000Jan01) / DaysInUniformLengthCentury;
- }
-
- static bool IsNegative(double value)
- {
- return Math.Sign(value) == -1;
- }
-
- 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
- static double EquationOfTime(double time)
- {
- double julianCenturies = JulianCenturies(time);
- double lambda = PolynomialSum(LambdaCoefficients, julianCenturies);
- double anomaly = PolynomialSum(AnomalyCoefficients, julianCenturies);
- double eccentricity = PolynomialSum(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);
- }
-
- 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
- static public double Midday(double date, double longitude)
- {
- return AsLocalTime(date+TwelveHours, longitude) - AsDayFraction(longitude);
- }
-
- static double InitLongitude(double longitude)
- {
- return NormalizeLongitude(longitude + HalfCircleOfArc) - HalfCircleOfArc;
- }
-
- // midday-in-tehran
- static public double MiddayAtPersianObservationSite(double date)
- {
- return Midday(date, InitLongitude(52.5)); // 52.5 degrees east - longitude of UTC+3:30 which defines Iranian Standard Time
- }
-
- static double PeriodicTerm(double julianCenturies, int x, double y, double z)
- {
- return x * SinOfDegree(y + z * julianCenturies);
- }
-
- 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;
- }
-
- static double Aberration(double julianCenturies)
- {
- return (0.0000974 * CosOfDegree(177.63 + (35999.01848 * julianCenturies))) - 0.005575;
- }
-
- static double Nutation(double julianCenturies)
- {
- double a = PolynomialSum(CoefficientsA, julianCenturies);
- double b = PolynomialSum(CoefficientsB, julianCenturies);
- return (-0.004778 * SinOfDegree(a)) - (0.0003667 * SinOfDegree(b));
- }
-
- static public 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);
- }
-
- static public double AsSeason(double longitude)
- {
- return (longitude < 0) ? (longitude + FullCircleOfArc) : longitude;
- }
-
- 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;
- }
- }
-}