1   /* Copyright 2002-2020 CS Group
2    * Licensed to CS Group (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.orekit.annotation.DefaultDataContext;
25  import org.orekit.data.DataContext;
26  import org.orekit.errors.OrekitException;
27  import org.orekit.errors.OrekitIllegalArgumentException;
28  import org.orekit.errors.OrekitMessages;
29  import org.orekit.utils.Constants;
30  
31  
32  /** This class represents a specific instant in time.
33  
34   * <p>Instances of this class are considered to be absolute in the sense
35   * that each one represent the occurrence of some event and can be compared
36   * to other instances or located in <em>any</em> {@link TimeScale time scale}. In
37   * other words the different locations of an event with respect to two different
38   * time scales (say {@link TAIScale TAI} and {@link UTCScale UTC} for example) are
39   * simply different perspective related to a single object. Only one
40   * <code>AbsoluteDate</code> instance is needed, both representations being available
41   * from this single instance by specifying the time scales as parameter when calling
42   * the ad-hoc methods.</p>
43   *
44   * <p>Since an instance is not bound to a specific time-scale, all methods related
45   * to the location of the date within some time scale require to provide the time
46   * scale as an argument. It is therefore possible to define a date in one time scale
47   * and to use it in another one. An example of such use is to read a date from a file
48   * in UTC and write it in another file in TAI. This can be done as follows:</p>
49   * <pre>
50   *   DateTimeComponents utcComponents = readNextDate();
51   *   AbsoluteDate date = new AbsoluteDate(utcComponents, TimeScalesFactory.getUTC());
52   *   writeNextDate(date.getComponents(TimeScalesFactory.getTAI()));
53   * </pre>
54   *
55   * <p>Two complementary views are available:</p>
56   * <ul>
57   *   <li><p>location view (mainly for input/output or conversions)</p>
58   *   <p>locations represent the coordinate of one event with respect to a
59   *   {@link TimeScale time scale}. The related methods are {@link
60   *   #AbsoluteDate(DateComponents, TimeComponents, TimeScale)}, {@link
61   *   #AbsoluteDate(int, int, int, int, int, double, TimeScale)}, {@link
62   *   #AbsoluteDate(int, int, int, TimeScale)}, {@link #AbsoluteDate(Date,
63   *   TimeScale)}, {@link #parseCCSDSCalendarSegmentedTimeCode(byte, byte[])},
64   *   {@link #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 #QZSS_EPOCH}
83   * {@link #J2000_EPOCH}, {@link #JAVA_EPOCH}.
84   * There are also two factory methods {@link #createJulianEpoch(double)}
85   * and {@link #createBesselianEpoch(double)} that can be used to compute other reference
86   * epochs like J1900.0 or B1950.0.
87   * In addition to these reference epochs, two other constants are defined for convenience:
88   * {@link #PAST_INFINITY} and {@link #FUTURE_INFINITY}, which can be used either as dummy
89   * dates when a date is not yet initialized, or for initialization of loops searching for
90   * a min or max date.
91   * </p>
92   * <p>
93   * Instances of the <code>AbsoluteDate</code> class are guaranteed to be immutable.
94   * </p>
95   * @author Luc Maisonobe
96   * @author Evan Ward
97   * @see TimeScale
98   * @see TimeStamped
99   * @see ChronologicalComparator
100  */
101 public class AbsoluteDate
102     implements TimeStamped, TimeShiftable<AbsoluteDate>, Comparable<AbsoluteDate>, Serializable {
103 
104     /** Reference epoch for julian dates: -4712-01-01T12:00:00 Terrestrial Time.
105      * <p>Both <code>java.util.Date</code> and {@link DateComponents} classes
106      * follow the astronomical conventions and consider a year 0 between
107      * years -1 and +1, hence this reference date lies in year -4712 and not
108      * in year -4713 as can be seen in other documents or programs that obey
109      * a different convention (for example the <code>convcal</code> utility).</p>
110      *
111      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
112      *
113      * @see TimeScales#getJulianEpoch()
114      */
115     @DefaultDataContext
116     public static final AbsoluteDate JULIAN_EPOCH =
117             DataContext.getDefault().getTimeScales().getJulianEpoch();
118 
119     /** Reference epoch for modified julian dates: 1858-11-17T00:00:00 Terrestrial Time.
120      *
121      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
122      *
123      * @see TimeScales#getModifiedJulianEpoch()
124      */
125     @DefaultDataContext
126     public static final AbsoluteDate MODIFIED_JULIAN_EPOCH =
127             DataContext.getDefault().getTimeScales().getModifiedJulianEpoch();
128 
129     /** Reference epoch for 1950 dates: 1950-01-01T00:00:00 Terrestrial Time.
130      *
131      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
132      *
133      * @see TimeScales#getFiftiesEpoch()
134      */
135     @DefaultDataContext
136     public static final AbsoluteDate FIFTIES_EPOCH =
137             DataContext.getDefault().getTimeScales().getFiftiesEpoch();
138 
139     /** Reference epoch for CCSDS Time Code Format (CCSDS 301.0-B-4):
140      * 1958-01-01T00:00:00 International Atomic Time (<em>not</em> UTC).
141      *
142      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
143      *
144      * @see TimeScales#getCcsdsEpoch()
145      */
146     @DefaultDataContext
147     public static final AbsoluteDate CCSDS_EPOCH =
148             DataContext.getDefault().getTimeScales().getCcsdsEpoch();
149 
150     /** Reference epoch for Galileo System Time: 1999-08-22T00:00:00 GST.
151      *
152      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
153      *
154      * @see TimeScales#getGalileoEpoch()
155      */
156     @DefaultDataContext
157     public static final AbsoluteDate GALILEO_EPOCH =
158             DataContext.getDefault().getTimeScales().getGalileoEpoch();
159 
160     /** Reference epoch for GPS weeks: 1980-01-06T00:00:00 GPS time.
161      *
162      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
163      *
164      * @see TimeScales#getGpsEpoch()
165      */
166     @DefaultDataContext
167     public static final AbsoluteDate GPS_EPOCH =
168             DataContext.getDefault().getTimeScales().getGpsEpoch();
169 
170     /** Reference epoch for QZSS weeks: 1980-01-06T00:00:00 QZSS time.
171      *
172      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
173      *
174      * @see TimeScales#getQzssEpoch()
175      */
176     @DefaultDataContext
177     public static final AbsoluteDate QZSS_EPOCH =
178             DataContext.getDefault().getTimeScales().getQzssEpoch();
179 
180     /** Reference epoch for IRNSS weeks: 1999-08-22T00:00:00 IRNSS time.
181      *
182      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
183      *
184      * @see TimeScales#getIrnssEpoch()
185      */
186     @DefaultDataContext
187     public static final AbsoluteDate IRNSS_EPOCH =
188             DataContext.getDefault().getTimeScales().getIrnssEpoch();
189 
190     /** Reference epoch for BeiDou weeks: 2006-01-01T00:00:00 UTC.
191      *
192      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
193      *
194      * @see TimeScales#getBeidouEpoch()
195      */
196     @DefaultDataContext
197     public static final AbsoluteDate BEIDOU_EPOCH =
198             DataContext.getDefault().getTimeScales().getBeidouEpoch();
199 
200     /** Reference epoch for GLONASS four-year interval number: 1996-01-01T00:00:00 GLONASS time.
201      * <p>By convention, TGLONASS = UTC + 3 hours.</p>
202      *
203      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
204      *
205      * @see TimeScales#getGlonassEpoch()
206      */
207     @DefaultDataContext
208     public static final AbsoluteDate GLONASS_EPOCH =
209             DataContext.getDefault().getTimeScales().getGlonassEpoch();
210 
211     /** J2000.0 Reference epoch: 2000-01-01T12:00:00 Terrestrial Time (<em>not</em> UTC).
212      * @see #createJulianEpoch(double)
213      * @see #createBesselianEpoch(double)
214      *
215      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
216      *
217      * @see TimeScales#getJ2000Epoch()
218      */
219     @DefaultDataContext
220     public static final AbsoluteDate J2000_EPOCH = // TODO
221             DataContext.getDefault().getTimeScales().getJ2000Epoch();
222 
223     /** Java Reference epoch: 1970-01-01T00:00:00 Universal Time Coordinate.
224      * <p>
225      * Between 1968-02-01 and 1972-01-01, UTC-TAI = 4.213 170 0s + (MJD - 39 126) x 0.002 592s.
226      * As on 1970-01-01 MJD = 40587, UTC-TAI = 8.000082s
227      * </p>
228      *
229      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
230      *
231      * @see TimeScales#getJavaEpoch()
232      */
233     @DefaultDataContext
234     public static final AbsoluteDate JAVA_EPOCH =
235             DataContext.getDefault().getTimeScales().getJavaEpoch();
236 
237     /**
238      * An arbitrary finite date. Uses when a non-null date is needed but its value doesn't
239      * matter.
240      */
241     public static final AbsoluteDate">AbsoluteDate ARBITRARY_EPOCH = new AbsoluteDate(0, 0);
242 
243     /** Dummy date at infinity in the past direction.
244      * @see TimeScales#getPastInfinity()
245      */
246     public static final AbsoluteDate PAST_INFINITY = ARBITRARY_EPOCH.shiftedBy(Double.NEGATIVE_INFINITY);
247 
248     /** Dummy date at infinity in the future direction.
249      * @see TimeScales#getFutureInfinity()
250      */
251     public static final AbsoluteDate FUTURE_INFINITY = ARBITRARY_EPOCH.shiftedBy(Double.POSITIVE_INFINITY);
252 
253     /** Serializable UID. */
254     private static final long serialVersionUID = 617061803741806846L;
255 
256     /** Reference epoch in seconds from 2000-01-01T12:00:00 TAI.
257      * <p>Beware, it is not {@link #J2000_EPOCH} since it is in TAI and not in TT.</p> */
258     private final long epoch;
259 
260     /** Offset from the reference epoch in seconds. */
261     private final double offset;
262 
263     /** Create an instance with a default value ({@link #J2000_EPOCH}).
264      *
265      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
266      *
267      * @see #AbsoluteDate(DateTimeComponents, TimeScale)
268      */
269     @DefaultDataContext
270     public AbsoluteDate() {
271         epoch  = J2000_EPOCH.epoch;
272         offset = J2000_EPOCH.offset;
273     }
274 
275     /** Build an instance from a location (parsed from a string) in a {@link TimeScale time scale}.
276      * <p>
277      * The supported formats for location are mainly the ones defined in ISO-8601 standard,
278      * the exact subset is explained in {@link DateTimeComponents#parseDateTime(String)},
279      * {@link DateComponents#parseDate(String)} and {@link TimeComponents#parseTime(String)}.
280      * </p>
281      * <p>
282      * As CCSDS ASCII calendar segmented time code is a trimmed down version of ISO-8601,
283      * it is also supported by this constructor.
284      * </p>
285      * @param location location in the time scale, must be in a supported format
286      * @param timeScale time scale
287      * @exception IllegalArgumentException if location string is not in a supported format
288      */
289     public AbsoluteDate(final String location, final TimeScale timeScale) {
290         this(DateTimeComponents.parseDateTime(location), timeScale);
291     }
292 
293     /** Build an instance from a location in a {@link TimeScale time scale}.
294      * @param location location in the time scale
295      * @param timeScale time scale
296      */
297     public AbsoluteDate(final DateTimeComponents location, final TimeScale timeScale) {
298         this(location.getDate(), location.getTime(), timeScale);
299     }
300 
301     /** Build an instance from a location in a {@link TimeScale time scale}.
302      * @param date date location in the time scale
303      * @param time time location in the time scale
304      * @param timeScale time scale
305      */
306     public AbsoluteDate(final DateComponents date, final TimeComponents time,
307                         final TimeScale timeScale) {
308 
309         final double seconds  = time.getSecond();
310         final double tsOffset = timeScale.offsetToTAI(date, time);
311 
312         // compute sum exactly, using Møller-Knuth TwoSum algorithm without branching
313         // the following statements must NOT be simplified, they rely on floating point
314         // arithmetic properties (rounding and representable numbers)
315         // at the end, the EXACT result of addition seconds + tsOffset
316         // is sum + residual, where sum is the closest representable number to the exact
317         // result and residual is the missing part that does not fit in the first number
318         final double sum      = seconds + tsOffset;
319         final double sPrime   = sum - tsOffset;
320         final double tPrime   = sum - sPrime;
321         final double deltaS   = seconds  - sPrime;
322         final double deltaT   = tsOffset - tPrime;
323         final double residual = deltaS   + deltaT;
324         final long   dl       = (long) FastMath.floor(sum);
325 
326         offset = (sum - dl) + residual;
327         epoch  = 60l * ((date.getJ2000Day() * 24l + time.getHour()) * 60l +
328                         time.getMinute() - time.getMinutesFromUTC() - 720l) + dl;
329 
330     }
331 
332     /** Build an instance from a location in a {@link TimeScale time scale}.
333      * @param year year number (may be 0 or negative for BC years)
334      * @param month month number from 1 to 12
335      * @param day day number from 1 to 31
336      * @param hour hour number from 0 to 23
337      * @param minute minute number from 0 to 59
338      * @param second second number from 0.0 to 60.0 (excluded)
339      * @param timeScale time scale
340      * @exception IllegalArgumentException if inconsistent arguments
341      * are given (parameters out of range)
342      */
343     public AbsoluteDate(final int year, final int month, final int day,
344                         final int hour, final int minute, final double second,
345                         final TimeScale timeScale) throws IllegalArgumentException {
346         this(new DateComponents(year, month, day), new TimeComponents(hour, minute, second), timeScale);
347     }
348 
349     /** Build an instance from a location in a {@link TimeScale time scale}.
350      * @param year year number (may be 0 or negative for BC years)
351      * @param month month enumerate
352      * @param day day number from 1 to 31
353      * @param hour hour number from 0 to 23
354      * @param minute minute number from 0 to 59
355      * @param second second number from 0.0 to 60.0 (excluded)
356      * @param timeScale time scale
357      * @exception IllegalArgumentException if inconsistent arguments
358      * are given (parameters out of range)
359      */
360     public AbsoluteDate(final int year, final Month month, final int day,
361                         final int hour, final int minute, final double second,
362                         final TimeScale timeScale) throws IllegalArgumentException {
363         this(new DateComponents(year, month, day), new TimeComponents(hour, minute, second), timeScale);
364     }
365 
366     /** Build an instance from a location in a {@link TimeScale time scale}.
367      * <p>The hour is set to 00:00:00.000.</p>
368      * @param date date location in the time scale
369      * @param timeScale time scale
370      * @exception IllegalArgumentException if inconsistent arguments
371      * are given (parameters out of range)
372      */
373     public AbsoluteDate(final DateComponents date, final TimeScale timeScale)
374         throws IllegalArgumentException {
375         this(date, TimeComponents.H00, timeScale);
376     }
377 
378     /** Build an instance from a location in a {@link TimeScale time scale}.
379      * <p>The hour is set to 00:00:00.000.</p>
380      * @param year year number (may be 0 or negative for BC years)
381      * @param month month number from 1 to 12
382      * @param day day number from 1 to 31
383      * @param timeScale time scale
384      * @exception IllegalArgumentException if inconsistent arguments
385      * are given (parameters out of range)
386      */
387     public AbsoluteDate(final int year, final int month, final int day,
388                         final TimeScale timeScale) throws IllegalArgumentException {
389         this(new DateComponents(year, month, day), TimeComponents.H00, timeScale);
390     }
391 
392     /** Build an instance from a location in a {@link TimeScale time scale}.
393      * <p>The hour is set to 00:00:00.000.</p>
394      * @param year year number (may be 0 or negative for BC years)
395      * @param month month enumerate
396      * @param day day number from 1 to 31
397      * @param timeScale time scale
398      * @exception IllegalArgumentException if inconsistent arguments
399      * are given (parameters out of range)
400      */
401     public AbsoluteDate(final int year, final Month month, final int day,
402                         final TimeScale timeScale) throws IllegalArgumentException {
403         this(new DateComponents(year, month, day), TimeComponents.H00, timeScale);
404     }
405 
406     /** Build an instance from a location in a {@link TimeScale time scale}.
407      * @param location location in the time scale
408      * @param timeScale time scale
409      */
410     public AbsoluteDate(final Date location, final TimeScale timeScale) {
411         this(new DateComponents(DateComponents.JAVA_EPOCH,
412                                 (int) (location.getTime() / 86400000l)),
413                                  millisToTimeComponents((int) (location.getTime() % 86400000l)),
414              timeScale);
415     }
416 
417     /** Build an instance from an elapsed duration since to another instant.
418      * <p>It is important to note that the elapsed duration is <em>not</em>
419      * the difference between two readings on a time scale. As an example,
420      * the duration between the two instants leading to the readings
421      * 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the {@link UTCScale UTC}
422      * time scale is <em>not</em> 1 second, but a stop watch would have measured
423      * an elapsed duration of 2 seconds between these two instances because a leap
424      * second was introduced at the end of 2005 in this time scale.</p>
425      * <p>This constructor is the reverse of the {@link #durationFrom(AbsoluteDate)}
426      * method.</p>
427      * @param since start instant of the measured duration
428      * @param elapsedDuration physically elapsed duration from the <code>since</code>
429      * instant, as measured in a regular time scale
430      * @see #durationFrom(AbsoluteDate)
431      */
432     public AbsoluteDatetml#AbsoluteDate">AbsoluteDate(final AbsoluteDate since, final double elapsedDuration) {
433 
434         final double sum = since.offset + elapsedDuration;
435         if (Double.isInfinite(sum)) {
436             offset = sum;
437             epoch  = (sum < 0) ? Long.MIN_VALUE : Long.MAX_VALUE;
438         } else {
439             // compute sum exactly, using Møller-Knuth TwoSum algorithm without branching
440             // the following statements must NOT be simplified, they rely on floating point
441             // arithmetic properties (rounding and representable numbers)
442             // at the end, the EXACT result of addition since.offset + elapsedDuration
443             // is sum + residual, where sum is the closest representable number to the exact
444             // result and residual is the missing part that does not fit in the first number
445             final double oPrime   = sum - elapsedDuration;
446             final double dPrime   = sum - oPrime;
447             final double deltaO   = since.offset - oPrime;
448             final double deltaD   = elapsedDuration - dPrime;
449             final double residual = deltaO + deltaD;
450             final long   dl       = (long) FastMath.floor(sum);
451             offset = (sum - dl) + residual;
452             epoch  = since.epoch  + dl;
453         }
454     }
455 
456     /** Build an instance from an apparent clock offset with respect to another
457      * instant <em>in the perspective of a specific {@link TimeScale time scale}</em>.
458      * <p>It is important to note that the apparent clock offset <em>is</em> the
459      * difference between two readings on a time scale and <em>not</em> an elapsed
460      * duration. As an example, the apparent clock offset between the two instants
461      * leading to the readings 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the
462      * {@link UTCScale UTC} time scale is 1 second, but the elapsed duration is 2
463      * seconds because a leap second has been introduced at the end of 2005 in this
464      * time scale.</p>
465      * <p>This constructor is the reverse of the {@link #offsetFrom(AbsoluteDate,
466      * TimeScale)} method.</p>
467      * @param reference reference instant
468      * @param apparentOffset apparent clock offset from the reference instant
469      * (difference between two readings in the specified time scale)
470      * @param timeScale time scale with respect to which the offset is defined
471      * @see #offsetFrom(AbsoluteDate, TimeScale)
472      */
473     public AbsoluteDatetml#AbsoluteDate">AbsoluteDate(final AbsoluteDate reference, final double apparentOffset,
474                         final TimeScale timeScale) {
475         this(new DateTimeComponents(reference.getComponents(timeScale), apparentOffset),
476              timeScale);
477     }
478 
479     /** Build a date from its internal components.
480      * <p>
481      * This method is reserved for internal used (for example by {@link FieldAbsoluteDate}).
482      * </p>
483      * @param epoch reference epoch in seconds from 2000-01-01T12:00:00 TAI.
484      * (beware, it is not {@link #J2000_EPOCH} since it is in TAI and not in TT)
485      * @param offset offset from the reference epoch in seconds (must be
486      * between 0.0 included and 1.0 excluded)
487      * @since 9.0
488      */
489     AbsoluteDate(final long epoch, final double offset) {
490         this.epoch  = epoch;
491         this.offset = offset;
492     }
493 
494     /** Extract time components from a number of milliseconds within the day.
495      * @param millisInDay number of milliseconds within the day
496      * @return time components
497      */
498     private static TimeComponents millisToTimeComponents(final int millisInDay) {
499         return new TimeComponents(millisInDay / 1000, 0.001 * (millisInDay % 1000));
500     }
501 
502     /** Get the reference epoch in seconds from 2000-01-01T12:00:00 TAI.
503      * <p>
504      * This method is reserved for internal used (for example by {@link FieldAbsoluteDate}).
505      * </p>
506      * <p>
507      * Beware, it is not {@link #J2000_EPOCH} since it is in TAI and not in TT.
508      * </p>
509      * @return reference epoch in seconds from 2000-01-01T12:00:00 TAI
510      * @since 9.0
511      */
512     long getEpoch() {
513         return epoch;
514     }
515 
516     /** Get the offset from the reference epoch in seconds.
517      * <p>
518      * This method is reserved for internal used (for example by {@link FieldAbsoluteDate}).
519      * </p>
520      * @return offset from the reference epoch in seconds
521      * @since 9.0
522      */
523     double getOffset() {
524         return offset;
525     }
526 
527     /** Build an instance from a CCSDS Unsegmented Time Code (CUC).
528      * <p>
529      * CCSDS Unsegmented Time Code is defined in the blue book:
530      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
531      * </p>
532      * <p>
533      * If the date to be parsed is formatted using version 3 of the standard
534      * (CCSDS 301.0-B-3 published in 2002) or if the extension of the preamble
535      * field introduced in version 4 of the standard is not used, then the
536      * {@code preambleField2} parameter can be set to 0.
537      * </p>
538      *
539      * <p>This method uses the {@link DataContext#getDefault() default data context} if
540      * the CCSDS epoch is used.
541      *
542      * @param preambleField1 first byte of the field specifying the format, often
543      * not transmitted in data interfaces, as it is constant for a given data interface
544      * @param preambleField2 second byte of the field specifying the format
545      * (added in revision 4 of the CCSDS standard in 2010), often not transmitted in data
546      * interfaces, as it is constant for a given data interface (value ignored if presence
547      * not signaled in {@code preambleField1})
548      * @param timeField byte array containing the time code
549      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
550      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
551      * may be null in this case)
552      * @return an instance corresponding to the specified date
553      * @see #parseCCSDSUnsegmentedTimeCode(byte, byte, byte[], AbsoluteDate, AbsoluteDate)
554      */
555     @DefaultDataContext
556     public static AbsoluteDate parseCCSDSUnsegmentedTimeCode(final byte preambleField1,
557                                                              final byte preambleField2,
558                                                              final byte[] timeField,
559                                                              final AbsoluteDate agencyDefinedEpoch) {
560         return parseCCSDSUnsegmentedTimeCode(preambleField1, preambleField2, timeField,
561                 agencyDefinedEpoch,
562                 DataContext.getDefault().getTimeScales().getCcsdsEpoch());
563     }
564 
565     /**
566      * Build an instance from a CCSDS Unsegmented Time Code (CUC).
567      * <p>
568      * CCSDS Unsegmented Time Code is defined in the blue book: CCSDS Time Code Format
569      * (CCSDS 301.0-B-4) published in November 2010
570      * </p>
571      * <p>
572      * If the date to be parsed is formatted using version 3 of the standard (CCSDS
573      * 301.0-B-3 published in 2002) or if the extension of the preamble field introduced
574      * in version 4 of the standard is not used, then the {@code preambleField2} parameter
575      * can be set to 0.
576      * </p>
577      *
578      * @param preambleField1     first byte of the field specifying the format, often not
579      *                           transmitted in data interfaces, as it is constant for a
580      *                           given data interface
581      * @param preambleField2     second byte of the field specifying the format (added in
582      *                           revision 4 of the CCSDS standard in 2010), often not
583      *                           transmitted in data interfaces, as it is constant for a
584      *                           given data interface (value ignored if presence not
585      *                           signaled in {@code preambleField1})
586      * @param timeField          byte array containing the time code
587      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field specifies
588      *                           the {@link #CCSDS_EPOCH CCSDS reference epoch} is used
589      *                           (and hence may be null in this case)
590      * @param ccsdsEpoch         reference epoch, ignored if the preamble field specifies
591      *                           the agency epoch is used.
592      * @return an instance corresponding to the specified date
593      * @since 10.1
594      */
595     public static AbsoluteDate parseCCSDSUnsegmentedTimeCode(
596             final byte preambleField1,
597             final byte preambleField2,
598             final byte[] timeField,
599             final AbsoluteDate agencyDefinedEpoch,
600             final AbsoluteDate ccsdsEpoch) {
601 
602         // time code identification and reference epoch
603         final AbsoluteDate epoch;
604         switch (preambleField1 & 0x70) {
605             case 0x10:
606                 // the reference epoch is CCSDS epoch 1958-01-01T00:00:00 TAI
607                 epoch = ccsdsEpoch;
608                 break;
609             case 0x20:
610                 // the reference epoch is agency defined
611                 if (agencyDefinedEpoch == null) {
612                     throw new OrekitException(OrekitMessages.CCSDS_DATE_MISSING_AGENCY_EPOCH);
613                 }
614                 epoch = agencyDefinedEpoch;
615                 break;
616             default :
617                 throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
618                                           formatByte(preambleField1));
619         }
620 
621         // time field lengths
622         int coarseTimeLength = 1 + ((preambleField1 & 0x0C) >>> 2);
623         int fineTimeLength   = preambleField1 & 0x03;
624 
625         if ((preambleField1 & 0x80) != 0x0) {
626             // there is an additional octet in preamble field
627             coarseTimeLength += (preambleField2 & 0x60) >>> 5;
628             fineTimeLength   += (preambleField2 & 0x1C) >>> 2;
629         }
630 
631         if (timeField.length != coarseTimeLength + fineTimeLength) {
632             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_LENGTH_TIME_FIELD,
633                                       timeField.length, coarseTimeLength + fineTimeLength);
634         }
635 
636         double seconds = 0;
637         for (int i = 0; i < coarseTimeLength; ++i) {
638             seconds = seconds * 256 + toUnsigned(timeField[i]);
639         }
640         double subseconds = 0;
641         for (int i = timeField.length - 1; i >= coarseTimeLength; --i) {
642             subseconds = (subseconds + toUnsigned(timeField[i])) / 256;
643         }
644 
645         return new AbsoluteDate(epoch, seconds).shiftedBy(subseconds);
646 
647     }
648 
649     /** Build an instance from a CCSDS Day Segmented Time Code (CDS).
650      * <p>
651      * CCSDS Day Segmented Time Code is defined in the blue book:
652      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
653      * </p>
654      *
655      * <p>This method uses the {@link DataContext#getDefault() default data context}.
656      *
657      * @param preambleField field specifying the format, often not transmitted in
658      * data interfaces, as it is constant for a given data interface
659      * @param timeField byte array containing the time code
660      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
661      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
662      * may be null in this case)
663      * @return an instance corresponding to the specified date
664      * @see #parseCCSDSDaySegmentedTimeCode(byte, byte[], DateComponents, TimeScale)
665      */
666     @DefaultDataContext
667     public static AbsoluteDate parseCCSDSDaySegmentedTimeCode(final byte preambleField, final byte[] timeField,
668                                                               final DateComponents agencyDefinedEpoch) {
669         return parseCCSDSDaySegmentedTimeCode(preambleField, timeField,
670                 agencyDefinedEpoch, DataContext.getDefault().getTimeScales().getUTC());
671     }
672 
673     /** Build an instance from a CCSDS Day Segmented Time Code (CDS).
674      * <p>
675      * CCSDS Day Segmented Time Code is defined in the blue book:
676      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
677      * </p>
678      * @param preambleField field specifying the format, often not transmitted in
679      * data interfaces, as it is constant for a given data interface
680      * @param timeField byte array containing the time code
681      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
682      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
683      * may be null in this case)
684      * @param utc      time scale used to compute date and time components.
685      * @return an instance corresponding to the specified date
686      * @since 10.1
687      */
688     public static AbsoluteDate parseCCSDSDaySegmentedTimeCode(
689             final byte preambleField,
690             final byte[] timeField,
691             final DateComponents agencyDefinedEpoch,
692             final TimeScale utc) {
693 
694         // time code identification
695         if ((preambleField & 0xF0) != 0x40) {
696             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
697                                       formatByte(preambleField));
698         }
699 
700         // reference epoch
701         final DateComponents epoch;
702         if ((preambleField & 0x08) == 0x00) {
703             // the reference epoch is CCSDS epoch 1958-01-01T00:00:00 TAI
704             epoch = DateComponents.CCSDS_EPOCH;
705         } else {
706             // the reference epoch is agency defined
707             if (agencyDefinedEpoch == null) {
708                 throw new OrekitException(OrekitMessages.CCSDS_DATE_MISSING_AGENCY_EPOCH);
709             }
710             epoch = agencyDefinedEpoch;
711         }
712 
713         // time field lengths
714         final int daySegmentLength = ((preambleField & 0x04) == 0x0) ? 2 : 3;
715         final int subMillisecondLength = (preambleField & 0x03) << 1;
716         if (subMillisecondLength == 6) {
717             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
718                                       formatByte(preambleField));
719         }
720         if (timeField.length != daySegmentLength + 4 + subMillisecondLength) {
721             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_LENGTH_TIME_FIELD,
722                                       timeField.length, daySegmentLength + 4 + subMillisecondLength);
723         }
724 
725 
726         int i   = 0;
727         int day = 0;
728         while (i < daySegmentLength) {
729             day = day * 256 + toUnsigned(timeField[i++]);
730         }
731 
732         long milliInDay = 0l;
733         while (i < daySegmentLength + 4) {
734             milliInDay = milliInDay * 256 + toUnsigned(timeField[i++]);
735         }
736         final int milli   = (int) (milliInDay % 1000l);
737         final int seconds = (int) ((milliInDay - milli) / 1000l);
738 
739         double subMilli = 0;
740         double divisor  = 1;
741         while (i < timeField.length) {
742             subMilli = subMilli * 256 + toUnsigned(timeField[i++]);
743             divisor *= 1000;
744         }
745 
746         final DateComponentsateComponents">DateComponents date = new DateComponents(epoch, day);
747         final TimeComponentsimeComponents">TimeComponents time = new TimeComponents(seconds);
748         return new AbsoluteDate(date, time, utc).shiftedBy(milli * 1.0e-3 + subMilli / divisor);
749 
750     }
751 
752     /** Build an instance from a CCSDS Calendar Segmented Time Code (CCS).
753      * <p>
754      * CCSDS Calendar Segmented Time Code is defined in the blue book:
755      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
756      * </p>
757      *
758      * <p>This method uses the {@link DataContext#getDefault() default data context}.
759      *
760      * @param preambleField field specifying the format, often not transmitted in
761      * data interfaces, as it is constant for a given data interface
762      * @param timeField byte array containing the time code
763      * @return an instance corresponding to the specified date
764      * @see #parseCCSDSCalendarSegmentedTimeCode(byte, byte[], TimeScale)
765      */
766     @DefaultDataContext
767     public static AbsoluteDate parseCCSDSCalendarSegmentedTimeCode(final byte preambleField, final byte[] timeField) {
768         return parseCCSDSCalendarSegmentedTimeCode(preambleField, timeField,
769                 DataContext.getDefault().getTimeScales().getUTC());
770     }
771 
772     /** Build an instance from a CCSDS Calendar Segmented Time Code (CCS).
773      * <p>
774      * CCSDS Calendar Segmented Time Code is defined in the blue book:
775      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
776      * </p>
777      * @param preambleField field specifying the format, often not transmitted in
778      * data interfaces, as it is constant for a given data interface
779      * @param timeField byte array containing the time code
780      * @param utc      time scale used to compute date and time components.
781      * @return an instance corresponding to the specified date
782      * @since 10.1
783      */
784     public static AbsoluteDate parseCCSDSCalendarSegmentedTimeCode(
785             final byte preambleField,
786             final byte[] timeField,
787             final TimeScale utc) {
788 
789         // time code identification
790         if ((preambleField & 0xF0) != 0x50) {
791             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
792                                       formatByte(preambleField));
793         }
794 
795         // time field length
796         final int length = 7 + (preambleField & 0x07);
797         if (length == 14) {
798             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_PREAMBLE_FIELD,
799                                       formatByte(preambleField));
800         }
801         if (timeField.length != length) {
802             throw new OrekitException(OrekitMessages.CCSDS_DATE_INVALID_LENGTH_TIME_FIELD,
803                                       timeField.length, length);
804         }
805 
806         // date part in the first four bytes
807         final DateComponents date;
808         if ((preambleField & 0x08) == 0x00) {
809             // month of year and day of month variation
810             date = new DateComponents(toUnsigned(timeField[0]) * 256 + toUnsigned(timeField[1]),
811                                       toUnsigned(timeField[2]),
812                                       toUnsigned(timeField[3]));
813         } else {
814             // day of year variation
815             date = new DateComponents(toUnsigned(timeField[0]) * 256 + toUnsigned(timeField[1]),
816                                       toUnsigned(timeField[2]) * 256 + toUnsigned(timeField[3]));
817         }
818 
819         // time part from bytes 5 to last (between 7 and 13 depending on precision)
820         final TimeComponentsimeComponents">TimeComponents time = new TimeComponents(toUnsigned(timeField[4]),
821                                                        toUnsigned(timeField[5]),
822                                                        toUnsigned(timeField[6]));
823         double subSecond = 0;
824         double divisor   = 1;
825         for (int i = 7; i < length; ++i) {
826             subSecond = subSecond * 100 + toUnsigned(timeField[i]);
827             divisor *= 100;
828         }
829 
830         return new AbsoluteDate(date, time, utc).shiftedBy(subSecond / divisor);
831 
832     }
833 
834     /** Decode a signed byte as an unsigned int value.
835      * @param b byte to decode
836      * @return an unsigned int value
837      */
838     private static int toUnsigned(final byte b) {
839         final int i = (int) b;
840         return (i < 0) ? 256 + i : i;
841     }
842 
843     /** Format a byte as an hex string for error messages.
844      * @param data byte to format
845      * @return a formatted string
846      */
847     private static String formatByte(final byte data) {
848         return "0x" + Integer.toHexString(data).toUpperCase();
849     }
850 
851     /** Build an instance corresponding to a Julian Day date.
852      * @param jd Julian day
853      * @param secondsSinceNoon seconds in the Julian day
854      * (BEWARE, Julian days start at noon, so 0.0 is noon)
855      * @param timeScale time scale in which the seconds in day are defined
856      * @return a new instant
857      */
858     public static AbsoluteDate createJDDate(final int jd, final double secondsSinceNoon,
859                                              final TimeScale timeScale) {
860         return new AbsoluteDate(new DateComponents(DateComponents.JULIAN_EPOCH, jd),
861                                 TimeComponents.H12, timeScale).shiftedBy(secondsSinceNoon);
862     }
863 
864     /** Build an instance corresponding to a Modified Julian Day date.
865      * @param mjd modified Julian day
866      * @param secondsInDay seconds in the day
867      * @param timeScale time scale in which the seconds in day are defined
868      * @return a new instant
869      * @exception OrekitIllegalArgumentException if seconds number is out of range
870      */
871     public static AbsoluteDate createMJDDate(final int mjd, final double secondsInDay,
872                                              final TimeScale timeScale)
873         throws OrekitIllegalArgumentException {
874         final DateComponents#DateComponents">DateComponents dc = new DateComponents(DateComponents.MODIFIED_JULIAN_EPOCH, mjd);
875         final TimeComponents tc;
876         if (secondsInDay >= Constants.JULIAN_DAY) {
877             // check we are really allowed to use this number of seconds
878             final int    secondsA = 86399; // 23:59:59, i.e. 59s in the last minute of the day
879             final double secondsB = secondsInDay - secondsA;
880             final TimeComponentseComponents">TimeComponents safeTC = new TimeComponents(secondsA, 0.0);
881             final AbsoluteDateuteDate">AbsoluteDate safeDate = new AbsoluteDate(dc, safeTC, timeScale);
882             if (timeScale.minuteDuration(safeDate) > 59 + secondsB) {
883                 // we are within the last minute of the day, the number of seconds is OK
884                 return safeDate.shiftedBy(secondsB);
885             } else {
886                 // let TimeComponents trigger an OrekitIllegalArgumentException
887                 // for the wrong number of seconds
888                 tc = new TimeComponents(secondsA, secondsB);
889             }
890         } else {
891             tc = new TimeComponents(secondsInDay);
892         }
893 
894         // create the date
895         return new AbsoluteDate(dc, tc, timeScale);
896 
897     }
898 
899 
900     /** Build an instance corresponding to a Julian Epoch (JE).
901      * <p>According to Lieske paper: <a
902      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
903      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
904      * vol. 73, no. 3, Mar. 1979, p. 282-284, Julian Epoch is related to Julian Ephemeris Date as:</p>
905      * <pre>
906      * JE = 2000.0 + (JED - 2451545.0) / 365.25
907      * </pre>
908      * <p>
909      * This method reverts the formula above and computes an {@code AbsoluteDate} from the Julian Epoch.
910      * </p>
911      *
912      * <p>This method uses the {@link DataContext#getDefault() default data context}.
913      *
914      * @param julianEpoch Julian epoch, like 2000.0 for defining the classical reference J2000.0
915      * @return a new instant
916      * @see #J2000_EPOCH
917      * @see #createBesselianEpoch(double)
918      * @see TimeScales#createJulianEpoch(double)
919      */
920     @DefaultDataContext
921     public static AbsoluteDate createJulianEpoch(final double julianEpoch) {
922         return DataContext.getDefault().getTimeScales().createJulianEpoch(julianEpoch);
923     }
924 
925     /** Build an instance corresponding to a Besselian Epoch (BE).
926      * <p>According to Lieske paper: <a
927      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
928      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
929      * vol. 73, no. 3, Mar. 1979, p. 282-284, Besselian Epoch is related to Julian Ephemeris Date as:</p>
930      * <pre>
931      * BE = 1900.0 + (JED - 2415020.31352) / 365.242198781
932      * </pre>
933      * <p>
934      * This method reverts the formula above and computes an {@code AbsoluteDate} from the Besselian Epoch.
935      * </p>
936      *
937      * <p>This method uses the {@link DataContext#getDefault() default data context}.
938      *
939      * @param besselianEpoch Besselian epoch, like 1950 for defining the classical reference B1950.0
940      * @return a new instant
941      * @see #createJulianEpoch(double)
942      * @see TimeScales#createBesselianEpoch(double)
943      */
944     @DefaultDataContext
945     public static AbsoluteDate createBesselianEpoch(final double besselianEpoch) {
946         return DataContext.getDefault().getTimeScales()
947                 .createBesselianEpoch(besselianEpoch);
948     }
949 
950     /** Get a time-shifted date.
951      * <p>
952      * Calling this method is equivalent to call <code>new AbsoluteDate(this, dt)</code>.
953      * </p>
954      * @param dt time shift in seconds
955      * @return a new date, shifted with respect to instance (which is immutable)
956      * @see org.orekit.utils.PVCoordinates#shiftedBy(double)
957      * @see org.orekit.attitudes.Attitude#shiftedBy(double)
958      * @see org.orekit.orbits.Orbit#shiftedBy(double)
959      * @see org.orekit.propagation.SpacecraftState#shiftedBy(double)
960      */
961     public AbsoluteDate shiftedBy(final double dt) {
962         return new AbsoluteDate(this, dt);
963     }
964 
965     /** Compute the physically elapsed duration between two instants.
966      * <p>The returned duration is the number of seconds physically
967      * elapsed between the two instants, measured in a regular time
968      * scale with respect to surface of the Earth (i.e either the {@link
969      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
970      * GPSScale GPS scale}). It is the only method that gives a
971      * duration with a physical meaning.</p>
972      * <p>This method gives the same result (with less computation)
973      * as calling {@link #offsetFrom(AbsoluteDate, TimeScale)}
974      * with a second argument set to one of the regular scales cited
975      * above.</p>
976      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
977      * double)} constructor.</p>
978      * @param instant instant to subtract from the instance
979      * @return offset in seconds between the two instants (positive
980      * if the instance is posterior to the argument)
981      * @see #offsetFrom(AbsoluteDate, TimeScale)
982      * @see #AbsoluteDate(AbsoluteDate, double)
983      */
984     public double durationFrom(final AbsoluteDate instant) {
985         return (epoch - instant.epoch) + (offset - instant.offset);
986     }
987 
988     /** Compute the apparent clock offset between two instant <em>in the
989      * perspective of a specific {@link TimeScale time scale}</em>.
990      * <p>The offset is the number of seconds counted in the given
991      * time scale between the locations of the two instants, with
992      * all time scale irregularities removed (i.e. considering all
993      * days are exactly 86400 seconds long). This method will give
994      * a result that may not have a physical meaning if the time scale
995      * is irregular. For example since a leap second was introduced at
996      * the end of 2005, the apparent offset between 2005-12-31T23:59:59
997      * and 2006-01-01T00:00:00 is 1 second, but the physical duration
998      * of the corresponding time interval as returned by the {@link
999      * #durationFrom(AbsoluteDate)} method is 2 seconds.</p>
1000      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
1001      * double, TimeScale)} constructor.</p>
1002      * @param instant instant to subtract from the instance
1003      * @param timeScale time scale with respect to which the offset should
1004      * be computed
1005      * @return apparent clock offset in seconds between the two instants
1006      * (positive if the instance is posterior to the argument)
1007      * @see #durationFrom(AbsoluteDate)
1008      * @see #AbsoluteDate(AbsoluteDate, double, TimeScale)
1009      */
1010     public double offsetFrom(final AbsoluteDate instant, final TimeScale timeScale) {
1011         final long   elapsedDurationA = epoch - instant.epoch;
1012         final double elapsedDurationB = (offset         + timeScale.offsetFromTAI(this)) -
1013                                         (instant.offset + timeScale.offsetFromTAI(instant));
1014         return  elapsedDurationA + elapsedDurationB;
1015     }
1016 
1017     /** Compute the offset between two time scales at the current instant.
1018      * <p>The offset is defined as <i>l₁-l₂</i>
1019      * where <i>l₁</i> is the location of the instant in
1020      * the <code>scale1</code> time scale and <i>l₂</i> is the
1021      * location of the instant in the <code>scale2</code> time scale.</p>
1022      * @param scale1 first time scale
1023      * @param scale2 second time scale
1024      * @return offset in seconds between the two time scales at the
1025      * current instant
1026      */
1027     public double timeScalesOffset(final TimeScaleScale">TimeScale scale1, final TimeScale scale2) {
1028         return scale1.offsetFromTAI(this) - scale2.offsetFromTAI(this);
1029     }
1030 
1031     /** Convert the instance to a Java {@link java.util.Date Date}.
1032      * <p>Conversion to the Date class induces a loss of precision because
1033      * the Date class does not provide sub-millisecond information. Java Dates
1034      * are considered to be locations in some times scales.</p>
1035      * @param timeScale time scale to use
1036      * @return a {@link java.util.Date Date} instance representing the location
1037      * of the instant in the time scale
1038      */
1039     public Date toDate(final TimeScale timeScale) {
1040         final double time = epoch + (offset + timeScale.offsetFromTAI(this));
1041         return new Date(FastMath.round((time + 10957.5 * 86400.0) * 1000));
1042     }
1043 
1044     /** Split the instance into date/time components.
1045      * @param timeScale time scale to use
1046      * @return date/time components
1047      */
1048     public DateTimeComponents getComponents(final TimeScale timeScale) {
1049 
1050         if (Double.isInfinite(offset)) {
1051             // special handling for past and future infinity
1052             if (offset < 0) {
1053                 return new DateTimeComponents(DateComponents.MIN_EPOCH, TimeComponents.H00);
1054             } else {
1055                 return new DateTimeComponents(DateComponents.MAX_EPOCH,
1056                                               new TimeComponents(23, 59, 59.999));
1057             }
1058         }
1059 
1060         // compute offset from 2000-01-01T00:00:00 in specified time scale exactly,
1061         // using Møller-Knuth TwoSum algorithm without branching
1062         // the following statements must NOT be simplified, they rely on floating point
1063         // arithmetic properties (rounding and representable numbers)
1064         // at the end, the EXACT result of addition offset + timeScale.offsetFromTAI(this)
1065         // is sum + residual, where sum is the closest representable number to the exact
1066         // result and residual is the missing part that does not fit in the first number
1067         final double taiOffset = timeScale.offsetFromTAI(this);
1068         final double sum       = offset + taiOffset;
1069         final double oPrime    = sum - taiOffset;
1070         final double dPrime    = sum - oPrime;
1071         final double deltaO    = offset - oPrime;
1072         final double deltaD    = taiOffset - dPrime;
1073         final double residual  = deltaO + deltaD;
1074 
1075         // split date and time
1076         final long   carry = (long) FastMath.floor(sum);
1077         double offset2000B = (sum - carry) + residual;
1078         long   offset2000A = epoch + carry + 43200l;
1079         if (offset2000B < 0) {
1080             offset2000A -= 1;
1081             offset2000B += 1;
1082         }
1083         long time = offset2000A % 86400l;
1084         if (time < 0l) {
1085             time += 86400l;
1086         }
1087         final int date = (int) ((offset2000A - time) / 86400l);
1088 
1089         // extract calendar elements
1090         final DateComponentsnts">DateComponents dateComponents = new DateComponents(DateComponents.J2000_EPOCH, date);
1091         TimeComponentsnts">TimeComponents timeComponents = new TimeComponents((int) time, offset2000B);
1092 
1093         if (timeScale.insideLeap(this)) {
1094             // fix the seconds number to take the leap into account
1095             timeComponents = new TimeComponents(timeComponents.getHour(), timeComponents.getMinute(),
1096                                                 timeComponents.getSecond() + timeScale.getLeap(this));
1097         }
1098 
1099         // build the components
1100         return new DateTimeComponents(dateComponents, timeComponents);
1101 
1102     }
1103 
1104     /** Split the instance into date/time components for a local time.
1105      *
1106      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1107      *
1108      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1109      * negative Westward UTC)
1110      * @return date/time components
1111      * @since 7.2
1112      * @see #getComponents(int, TimeScale)
1113      */
1114     @DefaultDataContext
1115     public DateTimeComponents getComponents(final int minutesFromUTC) {
1116         return getComponents(minutesFromUTC,
1117                 DataContext.getDefault().getTimeScales().getUTC());
1118     }
1119 
1120     /**
1121      * Split the instance into date/time components for a local time.
1122      *
1123      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1124      *                       negative Westward UTC)
1125      * @param utc            time scale used to compute date and time components.
1126      * @return date/time components
1127      * @since 10.1
1128      */
1129     public DateTimeComponents getComponents(final int minutesFromUTC,
1130                                             final TimeScale utc) {
1131 
1132         final DateTimeComponents utcComponents = getComponents(utc);
1133 
1134         // shift the date according to UTC offset, but WITHOUT touching the seconds,
1135         // as they may exceed 60.0 during a leap seconds introduction,
1136         // and we want to preserve these special cases
1137         final double seconds = utcComponents.getTime().getSecond();
1138 
1139         int minute = utcComponents.getTime().getMinute() + minutesFromUTC;
1140         final int hourShift;
1141         if (minute < 0) {
1142             hourShift = (minute - 59) / 60;
1143         } else if (minute > 59) {
1144             hourShift = minute / 60;
1145         } else {
1146             hourShift = 0;
1147         }
1148         minute -= 60 * hourShift;
1149 
1150         int hour = utcComponents.getTime().getHour() + hourShift;
1151         final int dayShift;
1152         if (hour < 0) {
1153             dayShift = (hour - 23) / 24;
1154         } else if (hour > 23) {
1155             dayShift = hour / 24;
1156         } else {
1157             dayShift = 0;
1158         }
1159         hour -= 24 * dayShift;
1160 
1161         return new DateTimeComponents(new DateComponents(utcComponents.getDate(), dayShift),
1162                                       new TimeComponents(hour, minute, seconds, minutesFromUTC));
1163 
1164     }
1165 
1166     /** Split the instance into date/time components for a time zone.
1167      *
1168      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1169      *
1170      * @param timeZone time zone
1171      * @return date/time components
1172      * @since 7.2
1173      * @see #getComponents(TimeZone, TimeScale)
1174      */
1175     @DefaultDataContext
1176     public DateTimeComponents getComponents(final TimeZone timeZone) {
1177         return getComponents(timeZone, DataContext.getDefault().getTimeScales().getUTC());
1178     }
1179 
1180     /**
1181      * Split the instance into date/time components for a time zone.
1182      *
1183      * @param timeZone time zone
1184      * @param utc      time scale used to computed date and time components.
1185      * @return date/time components
1186      * @since 10.1
1187      */
1188     public DateTimeComponents getComponents(final TimeZone timeZone,
1189                                             final TimeScale utc) {
1190         final AbsoluteDateteDate">AbsoluteDate javaEpoch = new AbsoluteDate(DateComponents.JAVA_EPOCH, utc);
1191         final long milliseconds = FastMath.round(1000 * offsetFrom(javaEpoch, utc));
1192         return getComponents(timeZone.getOffset(milliseconds) / 60000, utc);
1193     }
1194 
1195     /** Compare the instance with another date.
1196      * @param date other date to compare the instance to
1197      * @return a negative integer, zero, or a positive integer as this date
1198      * is before, simultaneous, or after the specified date.
1199      */
1200     public int compareTo(final AbsoluteDate date) {
1201         final double duration = durationFrom(date);
1202         if (!Double.isNaN(duration)) {
1203             return Double.compare(duration, 0.0);
1204         }
1205         // both dates are infinity or one is NaN or both are NaN
1206         return Double.compare(offset, date.offset);
1207     }
1208 
1209     /** {@inheritDoc} */
1210     public AbsoluteDate getDate() {
1211         return this;
1212     }
1213 
1214     /** Check if the instance represents the same time as another instance.
1215      * @param date other date
1216      * @return true if the instance and the other date refer to the same instant
1217      */
1218     public boolean equals(final Object date) {
1219 
1220         if (date == this) {
1221             // first fast check
1222             return true;
1223         }
1224 
1225         if ((date != null) && (date instanceof AbsoluteDate)) {
1226             return durationFrom((AbsoluteDate) date) == 0;
1227         }
1228 
1229         return false;
1230 
1231     }
1232 
1233     /** Check if the instance represents the same time as another.
1234      * @param other the instant to compare this date to
1235      * @return true if the instance and the argument refer to the same instant
1236      * @see #isCloseTo(TimeStamped, double)
1237      * @since 10.1
1238      */
1239     public boolean isEqualTo(final TimeStamped other) {
1240         return this.equals(other.getDate());
1241     }
1242 
1243     /** Check if the instance time is close to another.
1244      * @param other the instant to compare this date to
1245      * @param tolerance the separation, in seconds, under which the two instants will be considered close to each other
1246      * @return true if the duration between the instance and the argument is strictly below the tolerance
1247      * @see #isEqualTo(TimeStamped)
1248      * @since 10.1
1249      */
1250     public boolean isCloseTo(final TimeStamped other, final double tolerance) {
1251         return FastMath.abs(this.durationFrom(other.getDate())) < tolerance;
1252     }
1253 
1254     /** Check if the instance represents a time that is strictly before another.
1255      * @param other the instant to compare this date to
1256      * @return true if the instance is strictly before the argument when ordering chronologically
1257      * @see #isBeforeOrEqualTo(TimeStamped)
1258      * @since 10.1
1259      */
1260     public boolean isBefore(final TimeStamped other) {
1261         return this.compareTo(other.getDate()) < 0;
1262     }
1263 
1264     /** Check if the instance represents a time that is strictly after another.
1265      * @param other the instant to compare this date to
1266      * @return true if the instance is strictly after the argument when ordering chronologically
1267      * @see #isAfterOrEqualTo(TimeStamped)
1268      * @since 10.1
1269      */
1270     public boolean isAfter(final TimeStamped other) {
1271         return this.compareTo(other.getDate()) > 0;
1272     }
1273 
1274     /** Check if the instance represents a time that is before or equal to another.
1275      * @param other the instant to compare this date to
1276      * @return true if the instance is before (or equal to) the argument when ordering chronologically
1277      * @see #isBefore(TimeStamped)
1278      * @since 10.1
1279      */
1280     public boolean isBeforeOrEqualTo(final TimeStamped other) {
1281         return this.isEqualTo(other) || this.isBefore(other);
1282     }
1283 
1284     /** Check if the instance represents a time that is after or equal to another.
1285      * @param other the instant to compare this date to
1286      * @return true if the instance is after (or equal to) the argument when ordering chronologically
1287      * @see #isAfterOrEqualTo(TimeStamped)
1288      * @since 10.1
1289      */
1290     public boolean isAfterOrEqualTo(final TimeStamped other) {
1291         return this.isEqualTo(other) || this.isAfter(other);
1292     }
1293 
1294     /** Check if the instance represents a time that is strictly between two others representing
1295      * the boundaries of a time span. The two boundaries can be provided in any order: in other words,
1296      * whether <code>boundary</code> represents a time that is before or after <code>otherBoundary</code> will
1297      * not change the result of this method.
1298      * @param boundary one end of the time span
1299      * @param otherBoundary the other end of the time span
1300      * @return true if the instance is strictly between the two arguments when ordering chronologically
1301      * @see #isBetweenOrEqualTo(TimeStamped, TimeStamped)
1302      * @since 10.1
1303      */
1304     public boolean isBetween(final TimeStampedamped">TimeStamped boundary, final TimeStamped otherBoundary) {
1305         final TimeStamped beginning;
1306         final TimeStamped end;
1307         if (boundary.getDate().isBefore(otherBoundary)) {
1308             beginning = boundary;
1309             end = otherBoundary;
1310         } else {
1311             beginning = otherBoundary;
1312             end = boundary;
1313         }
1314         return this.isAfter(beginning) && this.isBefore(end);
1315     }
1316 
1317     /** Check if the instance represents a time that is between two others representing
1318      * the boundaries of a time span, or equal to one of them. The two boundaries can be provided in any order:
1319      * in other words, whether <code>boundary</code> represents a time that is before or after
1320      * <code>otherBoundary</code> will not change the result of this method.
1321      * @param boundary one end of the time span
1322      * @param otherBoundary the other end of the time span
1323      * @return true if the instance is between the two arguments (or equal to at least one of them)
1324      * when ordering chronologically
1325      * @see #isBetween(TimeStamped, TimeStamped)
1326      * @since 10.1
1327      */
1328     public boolean isBetweenOrEqualTo(final TimeStampedamped">TimeStamped boundary, final TimeStamped otherBoundary) {
1329         return this.isEqualTo(boundary) || this.isEqualTo(otherBoundary) || this.isBetween(boundary, otherBoundary);
1330     }
1331 
1332     /** Get a hashcode for this date.
1333      * @return hashcode
1334      */
1335     public int hashCode() {
1336         final long l = Double.doubleToLongBits(durationFrom(ARBITRARY_EPOCH));
1337         return (int) (l ^ (l >>> 32));
1338     }
1339 
1340     /** Get a String representation of the instant location in UTC time scale.
1341      *
1342      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1343      *
1344      * @return a string representation of the instance,
1345      * in ISO-8601 format with milliseconds accuracy
1346      * @see #toString(TimeScale)
1347      */
1348     @DefaultDataContext
1349     public String toString() {
1350         return toString(DataContext.getDefault().getTimeScales().getUTC());
1351     }
1352 
1353     /** Get a String representation of the instant location.
1354      * @param timeScale time scale to use
1355      * @return a string representation of the instance,
1356      * in ISO-8601 format with milliseconds accuracy
1357      */
1358     public String toString(final TimeScale timeScale) {
1359         return getComponents(timeScale).toString(timeScale.minuteDuration(this));
1360     }
1361 
1362     /** Get a String representation of the instant location for a local time.
1363      *
1364      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1365      *
1366      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1367      * negative Westward UTC).
1368      * @return string representation of the instance,
1369      * in ISO-8601 format with milliseconds accuracy
1370      * @since 7.2
1371      * @see #toString(int, TimeScale)
1372      */
1373     @DefaultDataContext
1374     public String toString(final int minutesFromUTC) {
1375         return toString(minutesFromUTC,
1376                 DataContext.getDefault().getTimeScales().getUTC());
1377     }
1378 
1379     /**
1380      * Get a String representation of the instant location for a local time.
1381      *
1382      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1383      *                       negative Westward UTC).
1384      * @param utc            time scale used to compute date and time components.
1385      * @return string representation of the instance, in ISO-8601 format with milliseconds
1386      * accuracy
1387      * @since 10.1
1388      */
1389     public String toString(final int minutesFromUTC, final TimeScale utc) {
1390         final int minuteDuration = utc.minuteDuration(this);
1391         return getComponents(minutesFromUTC, utc).toString(minuteDuration);
1392     }
1393 
1394     /** Get a String representation of the instant location for a time zone.
1395      *
1396      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1397      *
1398      * @param timeZone time zone
1399      * @return string representation of the instance,
1400      * in ISO-8601 format with milliseconds accuracy
1401      * @since 7.2
1402      * @see #toString(TimeZone, TimeScale)
1403      */
1404     @DefaultDataContext
1405     public String toString(final TimeZone timeZone) {
1406         return toString(timeZone, DataContext.getDefault().getTimeScales().getUTC());
1407     }
1408 
1409     /**
1410      * Get a String representation of the instant location for a time zone.
1411      *
1412      * @param timeZone time zone
1413      * @param utc      time scale used to compute date and time components.
1414      * @return string representation of the instance, in ISO-8601 format with milliseconds
1415      * accuracy
1416      * @since 10.1
1417      */
1418     public String toString(final TimeZone timeZone, final TimeScale utc) {
1419         final int minuteDuration = utc.minuteDuration(this);
1420         return getComponents(timeZone, utc).toString(minuteDuration);
1421     }
1422 
1423 }