1   /* Copyright 2002-2018 CS Systèmes d'Information
2    * Licensed to CS Systèmes d'Information (CS) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * CS licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *   http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.orekit.time;
18  
19  import java.io.Serializable;
20  import java.util.Date;
21  import java.util.TimeZone;
22  
23  import org.hipparchus.util.FastMath;
24  import org.hipparchus.util.MathArrays;
25  import org.orekit.errors.OrekitException;
26  import org.orekit.errors.OrekitIllegalArgumentException;
27  import org.orekit.errors.OrekitMessages;
28  import org.orekit.utils.Constants;
29  
30  
31  /** This class represents a specific instant in time.
32  
33   * <p>Instances of this class are considered to be absolute in the sense
34   * that each one represent the occurrence of some event and can be compared
35   * to other instances or located in <em>any</em> {@link TimeScale time scale}. In
36   * other words the different locations of an event with respect to two different
37   * time scales (say {@link TAIScale TAI} and {@link UTCScale UTC} for example) are
38   * simply different perspective related to a single object. Only one
39   * <code>AbsoluteDate</code> instance is needed, both representations being available
40   * from this single instance by specifying the time scales as parameter when calling
41   * the ad-hoc methods.</p>
42   *
43   * <p>Since an instance is not bound to a specific time-scale, all methods related
44   * to the location of the date within some time scale require to provide the time
45   * scale as an argument. It is therefore possible to define a date in one time scale
46   * and to use it in another one. An example of such use is to read a date from a file
47   * in UTC and write it in another file in TAI. This can be done as follows:</p>
48   * <pre>
49   *   DateTimeComponents utcComponents = readNextDate();
50   *   AbsoluteDate date = new AbsoluteDate(utcComponents, TimeScalesFactory.getUTC());
51   *   writeNextDate(date.getComponents(TimeScalesFactory.getTAI()));
52   * </pre>
53   *
54   * <p>Two complementary views are available:</p>
55   * <ul>
56   *   <li><p>location view (mainly for input/output or conversions)</p>
57   *   <p>locations represent the coordinate of one event with respect to a
58   *   {@link TimeScale time scale}. The related methods are {@link
59   *   #AbsoluteDate(DateComponents, TimeComponents, TimeScale)}, {@link
60   *   #AbsoluteDate(int, int, int, int, int, double, TimeScale)}, {@link
61   *   #AbsoluteDate(int, int, int, TimeScale)}, {@link #AbsoluteDate(Date,
62   *   TimeScale)}, {@link #createGPSDate(int, double)}, {@link
63   *   #parseCCSDSCalendarSegmentedTimeCode(byte, byte[])}, toString(){@link
64   *   #toDate(TimeScale)}, {@link #toString(TimeScale) toString(timeScale)},
65   *   {@link #toString()}, and {@link #timeScalesOffset}.</p>
66   *   </li>
67   *   <li><p>offset view (mainly for physical computation)</p>
68   *   <p>offsets represent either the flow of time between two events
69   *   (two instances of the class) or durations. They are counted in seconds,
70   *   are continuous and could be measured using only a virtually perfect stopwatch.
71   *   The related methods are {@link #AbsoluteDate(AbsoluteDate, double)},
72   *   {@link #parseCCSDSUnsegmentedTimeCode(byte, byte, byte[], AbsoluteDate)},
73   *   {@link #parseCCSDSDaySegmentedTimeCode(byte, byte[], DateComponents)},
74   *   {@link #durationFrom(AbsoluteDate)}, {@link #compareTo(AbsoluteDate)}, {@link #equals(Object)}
75   *   and {@link #hashCode()}.</p>
76   *   </li>
77   * </ul>
78   * <p>
79   * A few reference epochs which are commonly used in space systems have been defined. These
80   * epochs can be used as the basis for offset computation. The supported epochs are:
81   * {@link #JULIAN_EPOCH}, {@link #MODIFIED_JULIAN_EPOCH}, {@link #FIFTIES_EPOCH},
82   * {@link #CCSDS_EPOCH}, {@link #GALILEO_EPOCH}, {@link #GPS_EPOCH}, {@link #J2000_EPOCH},
83   * {@link #JAVA_EPOCH}. There are also two factory methods {@link #createJulianEpoch(double)}
84   * and {@link #createBesselianEpoch(double)} that can be used to compute other reference
85   * epochs like J1900.0 or B1950.0.
86   * In addition to these reference epochs, two other constants are defined for convenience:
87   * {@link #PAST_INFINITY} and {@link #FUTURE_INFINITY}, which can be used either as dummy
88   * dates when a date is not yet initialized, or for initialization of loops searching for
89   * a min or max date.
90   * </p>
91   * <p>
92   * Instances of the <code>AbsoluteDate</code> class are guaranteed to be immutable.
93   * </p>
94   * @author Luc Maisonobe
95   * @see TimeScale
96   * @see TimeStamped
97   * @see ChronologicalComparator
98   */
99  public class AbsoluteDate
100     implements TimeStamped, TimeShiftable<AbsoluteDate>, Comparable<AbsoluteDate>, Serializable {
101 
102     /** Reference epoch for julian dates: -4712-01-01T12:00:00 Terrestrial Time.
103      * <p>Both <code>java.util.Date</code> and {@link DateComponents} classes
104      * follow the astronomical conventions and consider a year 0 between
105      * years -1 and +1, hence this reference date lies in year -4712 and not
106      * in year -4713 as can be seen in other documents or programs that obey
107      * a different convention (for example the <code>convcal</code> utility).</p>
108      */
109     public static final AbsoluteDate JULIAN_EPOCH =
110         new AbsoluteDate(DateComponents.JULIAN_EPOCH, TimeComponents.H12, TimeScalesFactory.getTT());
111 
112     /** Reference epoch for modified julian dates: 1858-11-17T00:00:00 Terrestrial Time. */
113     public static final AbsoluteDate MODIFIED_JULIAN_EPOCH =
114         new AbsoluteDate(DateComponents.MODIFIED_JULIAN_EPOCH, TimeComponents.H00, TimeScalesFactory.getTT());
115 
116     /** Reference epoch for 1950 dates: 1950-01-01T00:00:00 Terrestrial Time. */
117     public static final AbsoluteDate FIFTIES_EPOCH =
118         new AbsoluteDate(DateComponents.FIFTIES_EPOCH, TimeComponents.H00, TimeScalesFactory.getTT());
119 
120     /** Reference epoch for CCSDS Time Code Format (CCSDS 301.0-B-4):
121      * 1958-01-01T00:00:00 International Atomic Time (<em>not</em> UTC). */
122     public static final AbsoluteDate CCSDS_EPOCH =
123         new AbsoluteDate(DateComponents.CCSDS_EPOCH, TimeComponents.H00, TimeScalesFactory.getTAI());
124 
125     /** Reference epoch for Galileo System Time: 1999-08-22T00:00:00 UTC. */
126     public static final AbsoluteDate GALILEO_EPOCH =
127         new AbsoluteDate(DateComponents.GALILEO_EPOCH, new TimeComponents(0, 0, 32),
128                          TimeScalesFactory.getTAI());
129 
130     /** Reference epoch for GPS weeks: 1980-01-06T00:00:00 GPS time. */
131     public static final AbsoluteDate GPS_EPOCH =
132         new AbsoluteDate(DateComponents.GPS_EPOCH, TimeComponents.H00, TimeScalesFactory.getGPS());
133 
134     /** J2000.0 Reference epoch: 2000-01-01T12:00:00 Terrestrial Time (<em>not</em> UTC).
135      * @see #createJulianEpoch(double)
136      * @see #createBesselianEpoch(double)
137      */
138     public static final AbsoluteDate J2000_EPOCH =
139         new AbsoluteDate(DateComponents.J2000_EPOCH, TimeComponents.H12, TimeScalesFactory.getTT());
140 
141     /** Java Reference epoch: 1970-01-01T00:00:00 Universal Time Coordinate.
142      * <p>
143      * Between 1968-02-01 and 1972-01-01, UTC-TAI = 4.213 170 0s + (MJD - 39 126) x 0.002 592s.
144      * As on 1970-01-01 MJD = 40587, UTC-TAI = 8.000082s
145      * </p>
146      */
147     public static final AbsoluteDate JAVA_EPOCH =
148         new AbsoluteDate(DateComponents.JAVA_EPOCH, TimeScalesFactory.getTAI()).shiftedBy(8.000082);
149 
150     /** Dummy date at infinity in the past direction. */
151     public static final AbsoluteDate PAST_INFINITY = JAVA_EPOCH.shiftedBy(Double.NEGATIVE_INFINITY);
152 
153     /** Dummy date at infinity in the future direction. */
154     public static final AbsoluteDate FUTURE_INFINITY = JAVA_EPOCH.shiftedBy(Double.POSITIVE_INFINITY);
155 
156     /** Serializable UID. */
157     private static final long serialVersionUID = 617061803741806846L;
158 
159     /** Reference epoch in seconds from 2000-01-01T12:00:00 TAI.
160      * <p>Beware, it is not {@link #J2000_EPOCH} since it is in TAI and not in TT.</p> */
161     private final long epoch;
162 
163     /** Offset from the reference epoch in seconds. */
164     private final double offset;
165 
166     /** Create an instance with a default value ({@link #J2000_EPOCH}).
167      */
168     public AbsoluteDate() {
169         epoch  = J2000_EPOCH.epoch;
170         offset = J2000_EPOCH.offset;
171     }
172 
173     /** Build an instance from a location (parsed from a string) in a {@link TimeScale time scale}.
174      * <p>
175      * The supported formats for location are mainly the ones defined in ISO-8601 standard,
176      * the exact subset is explained in {@link DateTimeComponents#parseDateTime(String)},
177      * {@link DateComponents#parseDate(String)} and {@link TimeComponents#parseTime(String)}.
178      * </p>
179      * <p>
180      * As CCSDS ASCII calendar segmented time code is a trimmed down version of ISO-8601,
181      * it is also supported by this constructor.
182      * </p>
183      * @param location location in the time scale, must be in a supported format
184      * @param timeScale time scale
185      * @exception IllegalArgumentException if location string is not in a supported format
186      */
187     public AbsoluteDate(final String location, final TimeScale timeScale) {
188         this(DateTimeComponents.parseDateTime(location), timeScale);
189     }
190 
191     /** Build an instance from a location in a {@link TimeScale time scale}.
192      * @param location location in the time scale
193      * @param timeScale time scale
194      */
195     public AbsoluteDate(final DateTimeComponents location, final TimeScale timeScale) {
196         this(location.getDate(), location.getTime(), timeScale);
197     }
198 
199     /** Build an instance from a location in a {@link TimeScale time scale}.
200      * @param date date location in the time scale
201      * @param time time location in the time scale
202      * @param timeScale time scale
203      */
204     public AbsoluteDate(final DateComponents date, final TimeComponents time,
205                         final TimeScale timeScale) {
206 
207         final double seconds  = time.getSecond();
208         final double tsOffset = timeScale.offsetToTAI(date, time);
209 
210         // compute sum exactly, using Møller-Knuth TwoSum algorithm without branching
211         // the following statements must NOT be simplified, they rely on floating point
212         // arithmetic properties (rounding and representable numbers)
213         // at the end, the EXACT result of addition seconds + tsOffset
214         // is sum + residual, where sum is the closest representable number to the exact
215         // result and residual is the missing part that does not fit in the first number
216         final double sum      = seconds + tsOffset;
217         final double sPrime   = sum - tsOffset;
218         final double tPrime   = sum - sPrime;
219         final double deltaS   = seconds  - sPrime;
220         final double deltaT   = tsOffset - tPrime;
221         final double residual = deltaS   + deltaT;
222         final long   dl       = (long) FastMath.floor(sum);
223 
224         offset = (sum - dl) + residual;
225         epoch  = 60l * ((date.getJ2000Day() * 24l + time.getHour()) * 60l +
226                         time.getMinute() - time.getMinutesFromUTC() - 720l) + dl;
227 
228     }
229 
230     /** Build an instance from a location in a {@link TimeScale time scale}.
231      * @param year year number (may be 0 or negative for BC years)
232      * @param month month number from 1 to 12
233      * @param day day number from 1 to 31
234      * @param hour hour number from 0 to 23
235      * @param minute minute number from 0 to 59
236      * @param second second number from 0.0 to 60.0 (excluded)
237      * @param timeScale time scale
238      * @exception IllegalArgumentException if inconsistent arguments
239      * are given (parameters out of range)
240      */
241     public AbsoluteDate(final int year, final int month, final int day,
242                         final int hour, final int minute, final double second,
243                         final TimeScale timeScale) throws IllegalArgumentException {
244         this(new DateComponents(year, month, day), new TimeComponents(hour, minute, second), timeScale);
245     }
246 
247     /** Build an instance from a location in a {@link TimeScale time scale}.
248      * @param year year number (may be 0 or negative for BC years)
249      * @param month month enumerate
250      * @param day day number from 1 to 31
251      * @param hour hour number from 0 to 23
252      * @param minute minute number from 0 to 59
253      * @param second second number from 0.0 to 60.0 (excluded)
254      * @param timeScale time scale
255      * @exception IllegalArgumentException if inconsistent arguments
256      * are given (parameters out of range)
257      */
258     public AbsoluteDate(final int year, final Month month, final int day,
259                         final int hour, final int minute, final double second,
260                         final TimeScale timeScale) throws IllegalArgumentException {
261         this(new DateComponents(year, month, day), new TimeComponents(hour, minute, second), timeScale);
262     }
263 
264     /** Build an instance from a location in a {@link TimeScale time scale}.
265      * <p>The hour is set to 00:00:00.000.</p>
266      * @param date date location in the time scale
267      * @param timeScale time scale
268      * @exception IllegalArgumentException if inconsistent arguments
269      * are given (parameters out of range)
270      */
271     public AbsoluteDate(final DateComponents date, final TimeScale timeScale)
272         throws IllegalArgumentException {
273         this(date, TimeComponents.H00, timeScale);
274     }
275 
276     /** Build an instance from a location in a {@link TimeScale time scale}.
277      * <p>The hour is set to 00:00:00.000.</p>
278      * @param year year number (may be 0 or negative for BC years)
279      * @param month month number from 1 to 12
280      * @param day day number from 1 to 31
281      * @param timeScale time scale
282      * @exception IllegalArgumentException if inconsistent arguments
283      * are given (parameters out of range)
284      */
285     public AbsoluteDate(final int year, final int month, final int day,
286                         final TimeScale timeScale) throws IllegalArgumentException {
287         this(new DateComponents(year, month, day), TimeComponents.H00, timeScale);
288     }
289 
290     /** Build an instance from a location in a {@link TimeScale time scale}.
291      * <p>The hour is set to 00:00:00.000.</p>
292      * @param year year number (may be 0 or negative for BC years)
293      * @param month month enumerate
294      * @param day day number from 1 to 31
295      * @param timeScale time scale
296      * @exception IllegalArgumentException if inconsistent arguments
297      * are given (parameters out of range)
298      */
299     public AbsoluteDate(final int year, final Month month, final int day,
300                         final TimeScale timeScale) throws IllegalArgumentException {
301         this(new DateComponents(year, month, day), TimeComponents.H00, timeScale);
302     }
303 
304     /** Build an instance from a location in a {@link TimeScale time scale}.
305      * @param location location in the time scale
306      * @param timeScale time scale
307      */
308     public AbsoluteDate(final Date location, final TimeScale timeScale) {
309         this(new DateComponents(DateComponents.JAVA_EPOCH,
310                                 (int) (location.getTime() / 86400000l)),
311                                 new TimeComponents(0.001 * (location.getTime() % 86400000l)),
312              timeScale);
313     }
314 
315     /** Build an instance from an elapsed duration since to another instant.
316      * <p>It is important to note that the elapsed duration is <em>not</em>
317      * the difference between two readings on a time scale. As an example,
318      * the duration between the two instants leading to the readings
319      * 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the {@link UTCScale UTC}
320      * time scale is <em>not</em> 1 second, but a stop watch would have measured
321      * an elapsed duration of 2 seconds between these two instances because a leap
322      * second was introduced at the end of 2005 in this time scale.</p>
323      * <p>This constructor is the reverse of the {@link #durationFrom(AbsoluteDate)}
324      * method.</p>
325      * @param since start instant of the measured duration
326      * @param elapsedDuration physically elapsed duration from the <code>since</code>
327      * instant, as measured in a regular time scale
328      * @see #durationFrom(AbsoluteDate)
329      */
330     public AbsoluteDate(final AbsoluteDate since, final double elapsedDuration) {
331 
332         final double sum = since.offset + elapsedDuration;
333         if (Double.isInfinite(sum)) {
334             offset = sum;
335             epoch  = (sum < 0) ? Long.MIN_VALUE : Long.MAX_VALUE;
336         } else {
337             // compute sum exactly, using Møller-Knuth TwoSum algorithm without branching
338             // the following statements must NOT be simplified, they rely on floating point
339             // arithmetic properties (rounding and representable numbers)
340             // at the end, the EXACT result of addition since.offset + elapsedDuration
341             // is sum + residual, where sum is the closest representable number to the exact
342             // result and residual is the missing part that does not fit in the first number
343             final double oPrime   = sum - elapsedDuration;
344             final double dPrime   = sum - oPrime;
345             final double deltaO   = since.offset - oPrime;
346             final double deltaD   = elapsedDuration - dPrime;
347             final double residual = deltaO + deltaD;
348             final long   dl       = (long) FastMath.floor(sum);
349             offset = (sum - dl) + residual;
350             epoch  = since.epoch  + dl;
351         }
352     }
353 
354     /** Build an instance from an apparent clock offset with respect to another
355      * instant <em>in the perspective of a specific {@link TimeScale time scale}</em>.
356      * <p>It is important to note that the apparent clock offset <em>is</em> the
357      * difference between two readings on a time scale and <em>not</em> an elapsed
358      * duration. As an example, the apparent clock offset between the two instants
359      * leading to the readings 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the
360      * {@link UTCScale UTC} time scale is 1 second, but the elapsed duration is 2
361      * seconds because a leap second has been introduced at the end of 2005 in this
362      * time scale.</p>
363      * <p>This constructor is the reverse of the {@link #offsetFrom(AbsoluteDate,
364      * TimeScale)} method.</p>
365      * @param reference reference instant
366      * @param apparentOffset apparent clock offset from the reference instant
367      * (difference between two readings in the specified time scale)
368      * @param timeScale time scale with respect to which the offset is defined
369      * @see #offsetFrom(AbsoluteDate, TimeScale)
370      */
371     public AbsoluteDate(final AbsoluteDate reference, final double apparentOffset,
372                         final TimeScale timeScale) {
373         this(new DateTimeComponents(reference.getComponents(timeScale), apparentOffset),
374              timeScale);
375     }
376 
377     /** Build a date from its internal components.
378      * <p>
379      * This method is reserved for internal used (for example by {@link FieldAbsoluteDate}).
380      * </p>
381      * @param epoch reference epoch in seconds from 2000-01-01T12:00:00 TAI.
382      * (beware, it is not {@link #J2000_EPOCH} since it is in TAI and not in TT)
383      * @param offset offset from the reference epoch in seconds (must be
384      * between 0.0 included and 1.0 excluded)
385      * @since 9.0
386      */
387     AbsoluteDate(final long epoch, final double offset) {
388         this.epoch  = epoch;
389         this.offset = offset;
390     }
391 
392     /** Get the reference epoch in seconds from 2000-01-01T12:00:00 TAI.
393      * <p>
394      * This method is reserved for internal used (for example by {@link FieldAbsoluteDate}).
395      * </p>
396      * <p>
397      * Beware, it is not {@link #J2000_EPOCH} since it is in TAI and not in TT.
398      * </p>
399      * @return reference epoch in seconds from 2000-01-01T12:00:00 TAI
400      * @since 9.0
401      */
402     long getEpoch() {
403         return epoch;
404     }
405 
406     /** Get the offset from the reference epoch in seconds.
407      * <p>
408      * This method is reserved for internal used (for example by {@link FieldAbsoluteDate}).
409      * </p>
410      * @return offset from the reference epoch in seconds
411      * @since 9.0
412      */
413     double getOffset() {
414         return offset;
415     }
416 
417     /** Build an instance from a CCSDS Unsegmented Time Code (CUC).
418      * <p>
419      * CCSDS Unsegmented Time Code is defined in the blue book:
420      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
421      * </p>
422      * <p>
423      * If the date to be parsed is formatted using version 3 of the standard
424      * (CCSDS 301.0-B-3 published in 2002) or if the extension of the preamble
425      * field introduced in version 4 of the standard is not used, then the
426      * {@code preambleField2} parameter can be set to 0.
427      * </p>
428      * @param preambleField1 first byte of the field specifying the format, often
429      * not transmitted in data interfaces, as it is constant for a given data interface
430      * @param preambleField2 second byte of the field specifying the format
431      * (added in revision 4 of the CCSDS standard in 2010), often not transmitted in data
432      * interfaces, as it is constant for a given data interface (value ignored if presence
433      * not signaled in {@code preambleField1})
434      * @param timeField byte array containing the time code
435      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
436      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
437      * may be null in this case)
438      * @return an instance corresponding to the specified date
439      * @throws OrekitException if preamble is inconsistent with Unsegmented Time Code,
440      * or if it is inconsistent with time field, or if agency epoch is needed but not provided
441      */
442     public static AbsoluteDate parseCCSDSUnsegmentedTimeCode(final byte preambleField1,
443                                                              final byte preambleField2,
444                                                              final byte[] timeField,
445                                                              final AbsoluteDate agencyDefinedEpoch)
446         throws OrekitException {
447 
448         // time code identification and reference epoch
449         final AbsoluteDate epoch;
450         switch (preambleField1 & 0x70) {
451             case 0x10:
452                 // the reference epoch is CCSDS epoch 1958-01-01T00:00:00 TAI
453                 epoch = CCSDS_EPOCH;
454                 break;
455             case 0x20:
456                 // the reference epoch is agency defined
457                 if (agencyDefinedEpoch == null) {
458                     throw new OrekitException(OrekitMessages.CCSDS_DATE_MISSING_AGENCY_EPOCH);
459                 }
460                 epoch = agencyDefinedEpoch;
461                 break;
462             default :
463                 throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
464                                           formatByte(preambleField1));
465         }
466 
467         // time field lengths
468         int coarseTimeLength = 1 + ((preambleField1 & 0x0C) >>> 2);
469         int fineTimeLength   = preambleField1 & 0x03;
470 
471         if ((preambleField1 & 0x80) != 0x0) {
472             // there is an additional octet in preamble field
473             coarseTimeLength += (preambleField2 & 0x60) >>> 5;
474             fineTimeLength   += (preambleField2 & 0x1C) >>> 2;
475         }
476 
477         if (timeField.length != coarseTimeLength + fineTimeLength) {
478             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_LENGTH_TIME_FIELD,
479                                       timeField.length, coarseTimeLength + fineTimeLength);
480         }
481 
482         double seconds = 0;
483         for (int i = 0; i < coarseTimeLength; ++i) {
484             seconds = seconds * 256 + toUnsigned(timeField[i]);
485         }
486         double subseconds = 0;
487         for (int i = timeField.length - 1; i >= coarseTimeLength; --i) {
488             subseconds = (subseconds + toUnsigned(timeField[i])) / 256;
489         }
490 
491         return new AbsoluteDate(epoch, seconds).shiftedBy(subseconds);
492 
493     }
494 
495     /** Build an instance from a CCSDS Day Segmented Time Code (CDS).
496      * <p>
497      * CCSDS Day Segmented Time Code is defined in the blue book:
498      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
499      * </p>
500      * @param preambleField field specifying the format, often not transmitted in
501      * data interfaces, as it is constant for a given data interface
502      * @param timeField byte array containing the time code
503      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
504      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
505      * may be null in this case)
506      * @return an instance corresponding to the specified date
507      * @throws OrekitException if preamble is inconsistent with Day Segmented Time Code,
508      * or if it is inconsistent with time field, or if agency epoch is needed but not provided,
509      * or it UTC time scale cannot be retrieved
510      */
511     public static AbsoluteDate parseCCSDSDaySegmentedTimeCode(final byte preambleField, final byte[] timeField,
512                                                               final DateComponents agencyDefinedEpoch)
513         throws OrekitException {
514 
515         // time code identification
516         if ((preambleField & 0xF0) != 0x40) {
517             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
518                                       formatByte(preambleField));
519         }
520 
521         // reference epoch
522         final DateComponents epoch;
523         if ((preambleField & 0x08) == 0x00) {
524             // the reference epoch is CCSDS epoch 1958-01-01T00:00:00 TAI
525             epoch = DateComponents.CCSDS_EPOCH;
526         } else {
527             // the reference epoch is agency defined
528             if (agencyDefinedEpoch == null) {
529                 throw new OrekitException(OrekitMessages.CCSDS_DATE_MISSING_AGENCY_EPOCH);
530             }
531             epoch = agencyDefinedEpoch;
532         }
533 
534         // time field lengths
535         final int daySegmentLength = ((preambleField & 0x04) == 0x0) ? 2 : 3;
536         final int subMillisecondLength = (preambleField & 0x03) << 1;
537         if (subMillisecondLength == 6) {
538             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
539                                       formatByte(preambleField));
540         }
541         if (timeField.length != daySegmentLength + 4 + subMillisecondLength) {
542             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_LENGTH_TIME_FIELD,
543                                       timeField.length, daySegmentLength + 4 + subMillisecondLength);
544         }
545 
546 
547         int i   = 0;
548         int day = 0;
549         while (i < daySegmentLength) {
550             day = day * 256 + toUnsigned(timeField[i++]);
551         }
552 
553         long milliInDay = 0l;
554         while (i < daySegmentLength + 4) {
555             milliInDay = milliInDay * 256 + toUnsigned(timeField[i++]);
556         }
557         final int milli   = (int) (milliInDay % 1000l);
558         final int seconds = (int) ((milliInDay - milli) / 1000l);
559 
560         double subMilli = 0;
561         double divisor  = 1;
562         while (i < timeField.length) {
563             subMilli = subMilli * 256 + toUnsigned(timeField[i++]);
564             divisor *= 1000;
565         }
566 
567         final DateComponents date = new DateComponents(epoch, day);
568         final TimeComponents time = new TimeComponents(seconds);
569         return new AbsoluteDate(date, time, TimeScalesFactory.getUTC()).shiftedBy(milli * 1.0e-3 + subMilli / divisor);
570 
571     }
572 
573     /** Build an instance from a CCSDS Calendar Segmented Time Code (CCS).
574      * <p>
575      * CCSDS Calendar Segmented Time Code is defined in the blue book:
576      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
577      * </p>
578      * @param preambleField field specifying the format, often not transmitted in
579      * data interfaces, as it is constant for a given data interface
580      * @param timeField byte array containing the time code
581      * @return an instance corresponding to the specified date
582      * @throws OrekitException if preamble is inconsistent with Calendar Segmented Time Code,
583      * or if it is inconsistent with time field, or it UTC time scale cannot be retrieved
584      */
585     public static AbsoluteDate parseCCSDSCalendarSegmentedTimeCode(final byte preambleField, final byte[] timeField)
586         throws OrekitException {
587 
588         // time code identification
589         if ((preambleField & 0xF0) != 0x50) {
590             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
591                                       formatByte(preambleField));
592         }
593 
594         // time field length
595         final int length = 7 + (preambleField & 0x07);
596         if (length == 14) {
597             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
598                                       formatByte(preambleField));
599         }
600         if (timeField.length != length) {
601             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_LENGTH_TIME_FIELD,
602                                       timeField.length, length);
603         }
604 
605         // date part in the first four bytes
606         final DateComponents date;
607         if ((preambleField & 0x08) == 0x00) {
608             // month of year and day of month variation
609             date = new DateComponents(toUnsigned(timeField[0]) * 256 + toUnsigned(timeField[1]),
610                                       toUnsigned(timeField[2]),
611                                       toUnsigned(timeField[3]));
612         } else {
613             // day of year variation
614             date = new DateComponents(toUnsigned(timeField[0]) * 256 + toUnsigned(timeField[1]),
615                                       toUnsigned(timeField[2]) * 256 + toUnsigned(timeField[3]));
616         }
617 
618         // time part from bytes 5 to last (between 7 and 13 depending on precision)
619         final TimeComponents time = new TimeComponents(toUnsigned(timeField[4]),
620                                                        toUnsigned(timeField[5]),
621                                                        toUnsigned(timeField[6]));
622         double subSecond = 0;
623         double divisor   = 1;
624         for (int i = 7; i < length; ++i) {
625             subSecond = subSecond * 100 + toUnsigned(timeField[i]);
626             divisor *= 100;
627         }
628 
629         return new AbsoluteDate(date, time, TimeScalesFactory.getUTC()).shiftedBy(subSecond / divisor);
630 
631     }
632 
633     /** Decode a signed byte as an unsigned int value.
634      * @param b byte to decode
635      * @return an unsigned int value
636      */
637     private static int toUnsigned(final byte b) {
638         final int i = (int) b;
639         return (i < 0) ? 256 + i : i;
640     }
641 
642     /** Format a byte as an hex string for error messages.
643      * @param data byte to format
644      * @return a formatted string
645      */
646     private static String formatByte(final byte data) {
647         return "0x" + Integer.toHexString(data).toUpperCase();
648     }
649 
650     /** Build an instance corresponding to a Julian Day date.
651      * @param jd Julian day
652      * @param secondsSinceNoon seconds in the Julian day
653      * (BEWARE, Julian days start at noon, so 0.0 is noon)
654      * @param timeScale time scale in which the seconds in day are defined
655      * @return a new instant
656      */
657     public static AbsoluteDate createJDDate(final int jd, final double secondsSinceNoon,
658                                              final TimeScale timeScale) {
659         return new AbsoluteDate(new DateComponents(DateComponents.JULIAN_EPOCH, jd),
660                                 TimeComponents.H12, timeScale).shiftedBy(secondsSinceNoon);
661     }
662 
663     /** Build an instance corresponding to a Modified Julian Day date.
664      * @param mjd modified Julian day
665      * @param secondsInDay seconds in the day
666      * @param timeScale time scale in which the seconds in day are defined
667      * @return a new instant
668      * @exception OrekitIllegalArgumentException if seconds number is out of range
669      */
670     public static AbsoluteDate createMJDDate(final int mjd, final double secondsInDay,
671                                              final TimeScale timeScale)
672         throws OrekitIllegalArgumentException {
673         final DateComponents dc = new DateComponents(DateComponents.MODIFIED_JULIAN_EPOCH, mjd);
674         final TimeComponents tc;
675         if (secondsInDay >= Constants.JULIAN_DAY) {
676             // check we are really allowed to use this number of seconds
677             final int    secondsA = 86399; // 23:59:59, i.e. 59s in the last minute of the day
678             final double secondsB = secondsInDay - secondsA;
679             final TimeComponents safeTC = new TimeComponents(secondsA, 0.0);
680             final AbsoluteDate safeDate = new AbsoluteDate(dc, safeTC, timeScale);
681             if (timeScale.minuteDuration(safeDate) > 59 + secondsB) {
682                 // we are within the last minute of the day, the number of seconds is OK
683                 return safeDate.shiftedBy(secondsB);
684             } else {
685                 // let TimeComponents trigger an OrekitIllegalArgumentException
686                 // for the wrong number of seconds
687                 tc = new TimeComponents(secondsA, secondsB);
688             }
689         } else {
690             tc = new TimeComponents(secondsInDay);
691         }
692 
693         // create the date
694         return new AbsoluteDate(dc, tc, timeScale);
695 
696     }
697 
698 
699     /** Build an instance corresponding to a GPS date.
700      * <p>GPS dates are provided as a week number starting at
701      * {@link #GPS_EPOCH GPS epoch} and as a number of milliseconds
702      * since week start.</p>
703      * @param weekNumber week number since {@link #GPS_EPOCH GPS epoch}
704      * @param milliInWeek number of milliseconds since week start
705      * @return a new instant
706      */
707     public static AbsoluteDate createGPSDate(final int weekNumber,
708                                              final double milliInWeek) {
709         final int day = (int) FastMath.floor(milliInWeek / (1000.0 * Constants.JULIAN_DAY));
710         final double secondsInDay = milliInWeek / 1000.0 - day * Constants.JULIAN_DAY;
711         return new AbsoluteDate(new DateComponents(DateComponents.GPS_EPOCH, weekNumber * 7 + day),
712                                 new TimeComponents(secondsInDay),
713                                 TimeScalesFactory.getGPS());
714     }
715 
716     /** Build an instance corresponding to a Julian Epoch (JE).
717      * <p>According to Lieske paper: <a
718      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&defaultprint=YES&filetype=.pdf.">
719      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
720      * vol. 73, no. 3, Mar. 1979, p. 282-284, Julian Epoch is related to Julian Ephemeris Date as:</p>
721      * <pre>
722      * JE = 2000.0 + (JED - 2451545.0) / 365.25
723      * </pre>
724      * <p>
725      * This method reverts the formula above and computes an {@code AbsoluteDate} from the Julian Epoch.
726      * </p>
727      * @param julianEpoch Julian epoch, like 2000.0 for defining the classical reference J2000.0
728      * @return a new instant
729      * @see #J2000_EPOCH
730      * @see #createBesselianEpoch(double)
731      */
732     public static AbsoluteDate createJulianEpoch(final double julianEpoch) {
733         return new AbsoluteDate(J2000_EPOCH,
734                                 Constants.JULIAN_YEAR * (julianEpoch - 2000.0));
735     }
736 
737     /** Build an instance corresponding to a Besselian Epoch (BE).
738      * <p>According to Lieske paper: <a
739      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&defaultprint=YES&filetype=.pdf.">
740      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
741      * vol. 73, no. 3, Mar. 1979, p. 282-284, Besselian Epoch is related to Julian Ephemeris Date as:</p>
742      * <pre>
743      * BE = 1900.0 + (JED - 2415020.31352) / 365.242198781
744      * </pre>
745      * <p>
746      * This method reverts the formula above and computes an {@code AbsoluteDate} from the Besselian Epoch.
747      * </p>
748      * @param besselianEpoch Besselian epoch, like 1950 for defining the classical reference B1950.0
749      * @return a new instant
750      * @see #createJulianEpoch(double)
751      */
752     public static AbsoluteDate createBesselianEpoch(final double besselianEpoch) {
753         return new AbsoluteDate(J2000_EPOCH,
754                                 MathArrays.linearCombination(Constants.BESSELIAN_YEAR, besselianEpoch - 1900,
755                                                              Constants.JULIAN_DAY, -36525,
756                                                              Constants.JULIAN_DAY, 0.31352));
757     }
758 
759     /** Get a time-shifted date.
760      * <p>
761      * Calling this method is equivalent to call <code>new AbsoluteDate(this, dt)</code>.
762      * </p>
763      * @param dt time shift in seconds
764      * @return a new date, shifted with respect to instance (which is immutable)
765      * @see org.orekit.utils.PVCoordinates#shiftedBy(double)
766      * @see org.orekit.attitudes.Attitude#shiftedBy(double)
767      * @see org.orekit.orbits.Orbit#shiftedBy(double)
768      * @see org.orekit.propagation.SpacecraftState#shiftedBy(double)
769      */
770     public AbsoluteDate shiftedBy(final double dt) {
771         return new AbsoluteDate(this, dt);
772     }
773 
774     /** Compute the physically elapsed duration between two instants.
775      * <p>The returned duration is the number of seconds physically
776      * elapsed between the two instants, measured in a regular time
777      * scale with respect to surface of the Earth (i.e either the {@link
778      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
779      * GPSScale GPS scale}). It is the only method that gives a
780      * duration with a physical meaning.</p>
781      * <p>This method gives the same result (with less computation)
782      * as calling {@link #offsetFrom(AbsoluteDate, TimeScale)}
783      * with a second argument set to one of the regular scales cited
784      * above.</p>
785      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
786      * double)} constructor.</p>
787      * @param instant instant to subtract from the instance
788      * @return offset in seconds between the two instants (positive
789      * if the instance is posterior to the argument)
790      * @see #offsetFrom(AbsoluteDate, TimeScale)
791      * @see #AbsoluteDate(AbsoluteDate, double)
792      */
793     public double durationFrom(final AbsoluteDate instant) {
794         return (epoch - instant.epoch) + (offset - instant.offset);
795     }
796 
797     /** Compute the apparent clock offset between two instant <em>in the
798      * perspective of a specific {@link TimeScale time scale}</em>.
799      * <p>The offset is the number of seconds counted in the given
800      * time scale between the locations of the two instants, with
801      * all time scale irregularities removed (i.e. considering all
802      * days are exactly 86400 seconds long). This method will give
803      * a result that may not have a physical meaning if the time scale
804      * is irregular. For example since a leap second was introduced at
805      * the end of 2005, the apparent offset between 2005-12-31T23:59:59
806      * and 2006-01-01T00:00:00 is 1 second, but the physical duration
807      * of the corresponding time interval as returned by the {@link
808      * #durationFrom(AbsoluteDate)} method is 2 seconds.</p>
809      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
810      * double, TimeScale)} constructor.</p>
811      * @param instant instant to subtract from the instance
812      * @param timeScale time scale with respect to which the offset should
813      * be computed
814      * @return apparent clock offset in seconds between the two instants
815      * (positive if the instance is posterior to the argument)
816      * @see #durationFrom(AbsoluteDate)
817      * @see #AbsoluteDate(AbsoluteDate, double, TimeScale)
818      */
819     public double offsetFrom(final AbsoluteDate instant, final TimeScale timeScale) {
820         final long   elapsedDurationA = epoch - instant.epoch;
821         final double elapsedDurationB = (offset         + timeScale.offsetFromTAI(this)) -
822                                         (instant.offset + timeScale.offsetFromTAI(instant));
823         return  elapsedDurationA + elapsedDurationB;
824     }
825 
826     /** Compute the offset between two time scales at the current instant.
827      * <p>The offset is defined as <i>l₁-l₂</i>
828      * where <i>l₁</i> is the location of the instant in
829      * the <code>scale1</code> time scale and <i>l₂</i> is the
830      * location of the instant in the <code>scale2</code> time scale.</p>
831      * @param scale1 first time scale
832      * @param scale2 second time scale
833      * @return offset in seconds between the two time scales at the
834      * current instant
835      */
836     public double timeScalesOffset(final TimeScale scale1, final TimeScale scale2) {
837         return scale1.offsetFromTAI(this) - scale2.offsetFromTAI(this);
838     }
839 
840     /** Convert the instance to a Java {@link java.util.Date Date}.
841      * <p>Conversion to the Date class induces a loss of precision because
842      * the Date class does not provide sub-millisecond information. Java Dates
843      * are considered to be locations in some times scales.</p>
844      * @param timeScale time scale to use
845      * @return a {@link java.util.Date Date} instance representing the location
846      * of the instant in the time scale
847      */
848     public Date toDate(final TimeScale timeScale) {
849         final double time = epoch + (offset + timeScale.offsetFromTAI(this));
850         return new Date(FastMath.round((time + 10957.5 * 86400.0) * 1000));
851     }
852 
853     /** Split the instance into date/time components.
854      * @param timeScale time scale to use
855      * @return date/time components
856      */
857     public DateTimeComponents getComponents(final TimeScale timeScale) {
858 
859         if (Double.isInfinite(offset)) {
860             // special handling for past and future infinity
861             if (offset < 0) {
862                 return new DateTimeComponents(DateComponents.MIN_EPOCH, TimeComponents.H00);
863             } else {
864                 return new DateTimeComponents(DateComponents.MAX_EPOCH,
865                                               new TimeComponents(23, 59, 59.999));
866             }
867         }
868 
869         // compute offset from 2000-01-01T00:00:00 in specified time scale exactly,
870         // using Møller-Knuth TwoSum algorithm without branching
871         // the following statements must NOT be simplified, they rely on floating point
872         // arithmetic properties (rounding and representable numbers)
873         // at the end, the EXACT result of addition offset + timeScale.offsetFromTAI(this)
874         // is sum + residual, where sum is the closest representable number to the exact
875         // result and residual is the missing part that does not fit in the first number
876         final double taiOffset = timeScale.offsetFromTAI(this);
877         final double sum       = offset + taiOffset;
878         final double oPrime    = sum - taiOffset;
879         final double dPrime    = sum - oPrime;
880         final double deltaO    = offset - oPrime;
881         final double deltaD    = taiOffset - dPrime;
882         final double residual  = deltaO + deltaD;
883 
884         // split date and time
885         final long   carry = (long) FastMath.floor(sum);
886         double offset2000B = (sum - carry) + residual;
887         long   offset2000A = epoch + carry + 43200l;
888         if (offset2000B < 0) {
889             offset2000A -= 1;
890             offset2000B += 1;
891         }
892         long time = offset2000A % 86400l;
893         if (time < 0l) {
894             time += 86400l;
895         }
896         final int date = (int) ((offset2000A - time) / 86400l);
897 
898         // extract calendar elements
899         final DateComponents dateComponents = new DateComponents(DateComponents.J2000_EPOCH, date);
900         TimeComponents timeComponents = new TimeComponents((int) time, offset2000B);
901 
902         if (timeScale.insideLeap(this)) {
903             // fix the seconds number to take the leap into account
904             timeComponents = new TimeComponents(timeComponents.getHour(), timeComponents.getMinute(),
905                                                 timeComponents.getSecond() + timeScale.getLeap(this));
906         }
907 
908         // build the components
909         return new DateTimeComponents(dateComponents, timeComponents);
910 
911     }
912 
913     /** Split the instance into date/time components for a local time.
914      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
915      * negative Westward UTC)
916      * @return date/time components
917      * @exception OrekitException if UTC time scale cannot be retrieved
918      * @since 7.2
919      */
920     public DateTimeComponents getComponents(final int minutesFromUTC)
921         throws OrekitException {
922 
923         final DateTimeComponents utcComponents = getComponents(TimeScalesFactory.getUTC());
924 
925         // shift the date according to UTC offset, but WITHOUT touching the seconds,
926         // as they may exceed 60.0 during a leap seconds introduction,
927         // and we want to preserve these special cases
928         final double seconds = utcComponents.getTime().getSecond();
929 
930         int minute = utcComponents.getTime().getMinute() + minutesFromUTC;
931         final int hourShift;
932         if (minute < 0) {
933             hourShift = (minute - 59) / 60;
934         } else if (minute > 59) {
935             hourShift = minute / 60;
936         } else {
937             hourShift = 0;
938         }
939         minute -= 60 * hourShift;
940 
941         int hour = utcComponents.getTime().getHour() + hourShift;
942         final int dayShift;
943         if (hour < 0) {
944             dayShift = (hour - 23) / 24;
945         } else if (hour > 23) {
946             dayShift = hour / 24;
947         } else {
948             dayShift = 0;
949         }
950         hour -= 24 * dayShift;
951 
952         return new DateTimeComponents(new DateComponents(utcComponents.getDate(), dayShift),
953                                       new TimeComponents(hour, minute, seconds, minutesFromUTC));
954 
955     }
956 
957     /** Split the instance into date/time components for a time zone.
958      * @param timeZone time zone
959      * @return date/time components
960      * @exception OrekitException if UTC time scale cannot be retrieved
961      * @since 7.2
962      */
963     public DateTimeComponents getComponents(final TimeZone timeZone)
964         throws OrekitException {
965         final long milliseconds = FastMath.round(1000 * offsetFrom(JAVA_EPOCH, TimeScalesFactory.getUTC()));
966         return getComponents(timeZone.getOffset(milliseconds) / 60000);
967     }
968 
969     /** Compare the instance with another date.
970      * @param date other date to compare the instance to
971      * @return a negative integer, zero, or a positive integer as this date
972      * is before, simultaneous, or after the specified date.
973      */
974     public int compareTo(final AbsoluteDate date) {
975         return Double.compare(durationFrom(date),  0);
976     }
977 
978     /** {@inheritDoc} */
979     public AbsoluteDate getDate() {
980         return this;
981     }
982 
983     /** Check if the instance represent the same time as another instance.
984      * @param date other date
985      * @return true if the instance and the other date refer to the same instant
986      */
987     public boolean equals(final Object date) {
988 
989         if (date == this) {
990             // first fast check
991             return true;
992         }
993 
994         if ((date != null) && (date instanceof AbsoluteDate)) {
995             return durationFrom((AbsoluteDate) date) == 0;
996         }
997 
998         return false;
999 
1000     }
1001 
1002     /** Get a hashcode for this date.
1003      * @return hashcode
1004      */
1005     public int hashCode() {
1006         final long l = Double.doubleToLongBits(durationFrom(J2000_EPOCH));
1007         return (int) (l ^ (l >>> 32));
1008     }
1009 
1010     /** Get a String representation of the instant location in UTC time scale.
1011      * @return a string representation of the instance,
1012      * in ISO-8601 format with milliseconds accuracy
1013      */
1014     public String toString() {
1015         try {
1016             return toString(TimeScalesFactory.getUTC());
1017         } catch (OrekitException oe) {
1018             throw new RuntimeException(oe);
1019         }
1020     }
1021 
1022     /** Get a String representation of the instant location.
1023      * @param timeScale time scale to use
1024      * @return a string representation of the instance,
1025      * in ISO-8601 format with milliseconds accuracy
1026      */
1027     public String toString(final TimeScale timeScale) {
1028         return getComponents(timeScale).toString(timeScale.minuteDuration(this));
1029     }
1030 
1031     /** Get a String representation of the instant location for a local time.
1032      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1033      * negative Westward UTC).
1034      * @return string representation of the instance,
1035      * in ISO-8601 format with milliseconds accuracy
1036      * @exception OrekitException if UTC time scale cannot be retrieved
1037      * @since 7.2
1038      */
1039     public String toString(final int minutesFromUTC)
1040         throws OrekitException {
1041         final int minuteDuration = TimeScalesFactory.getUTC().minuteDuration(this);
1042         return getComponents(minutesFromUTC).toString(minuteDuration);
1043     }
1044 
1045     /** Get a String representation of the instant location for a time zone.
1046      * @param timeZone time zone
1047      * @return string representation of the instance,
1048      * in ISO-8601 format with milliseconds accuracy
1049      * @exception OrekitException if UTC time scale cannot be retrieved
1050      * @since 7.2
1051      */
1052     public String toString(final TimeZone timeZone)
1053         throws OrekitException {
1054         final int minuteDuration = TimeScalesFactory.getUTC().minuteDuration(this);
1055         return getComponents(timeZone).toString(minuteDuration);
1056     }
1057 
1058 }