1   /* Copyright 2002-2024 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.time.Instant;
20  import java.time.LocalDateTime;
21  import java.time.ZoneOffset;
22  import java.time.format.DateTimeFormatter;
23  import java.util.Date;
24  import java.util.TimeZone;
25  
26  import java.util.concurrent.TimeUnit;
27  import org.hipparchus.CalculusFieldElement;
28  import org.hipparchus.Field;
29  import org.hipparchus.FieldElement;
30  import org.hipparchus.analysis.differentiation.Derivative;
31  import org.hipparchus.complex.Complex;
32  import org.hipparchus.util.FastMath;
33  import org.hipparchus.util.MathUtils;
34  import org.hipparchus.util.MathUtils.FieldSumAndResidual;
35  import org.hipparchus.util.MathUtils.SumAndResidual;
36  import org.orekit.annotation.DefaultDataContext;
37  import org.orekit.data.DataContext;
38  import org.orekit.utils.Constants;
39  
40  /** This class represents a specific instant in time.
41  
42   * <p>Instances of this class are considered to be absolute in the sense
43   * that each one represent the occurrence of some event and can be compared
44   * to other instances or located in <em>any</em> {@link TimeScale time scale}. In
45   * other words the different locations of an event with respect to two different
46   * time scales (say {@link TAIScale TAI} and {@link UTCScale UTC} for example) are
47   * simply different perspective related to a single object. Only one
48   * <code>FieldAbsoluteDate&lt;T&gt;</code> instance is needed, both representations being available
49   * from this single instance by specifying the time scales as parameter when calling
50   * the ad-hoc methods.</p>
51   *
52   * <p>Since an instance is not bound to a specific time-scale, all methods related
53   * to the location of the date within some time scale require to provide the time
54   * scale as an argument. It is therefore possible to define a date in one time scale
55   * and to use it in another one. An example of such use is to read a date from a file
56   * in UTC and write it in another file in TAI. This can be done as follows:</p>
57   * <pre>
58   *   DateTimeComponents utcComponents = readNextDate();
59   *   FieldAbsoluteDate&lt;T&gt; date = new FieldAbsoluteDate&lt;&gt;(utcComponents, TimeScalesFactory.getUTC());
60   *   writeNextDate(date.getComponents(TimeScalesFactory.getTAI()));
61   * </pre>
62   *
63   * <p>Two complementary views are available:</p>
64   * <ul>
65   *   <li><p>location view (mainly for input/output or conversions)</p>
66   *   <p>locations represent the coordinate of one event with respect to a
67   *   {@link TimeScale time scale}. The related methods are {@link
68   *   #FieldAbsoluteDate(Field, DateComponents, TimeComponents, TimeScale)}, {@link
69   *   #FieldAbsoluteDate(Field, int, int, int, int, int, double, TimeScale)}, {@link
70   *   #FieldAbsoluteDate(Field, int, int, int, TimeScale)}, {@link #FieldAbsoluteDate(Field,
71   *   Date, TimeScale)}, {@link #createGPSDate(int, CalculusFieldElement)}, {@link
72   *   #parseCCSDSCalendarSegmentedTimeCode(byte, byte[])}, {@link #toDate(TimeScale)},
73   *   {@link #toString(TimeScale) toString(timeScale)}, {@link #toString()},
74   *   and {@link #timeScalesOffset}.</p>
75   *   </li>
76   *   <li><p>offset view (mainly for physical computation)</p>
77   *   <p>offsets represent either the flow of time between two events
78   *   (two instances of the class) or durations. They are counted in seconds,
79   *   are continuous and could be measured using only a virtually perfect stopwatch.
80   *   The related methods are {@link #FieldAbsoluteDate(FieldAbsoluteDate, double)},
81   *   {@link #parseCCSDSUnsegmentedTimeCode(Field, byte, byte, byte[], FieldAbsoluteDate)},
82   *   {@link #parseCCSDSDaySegmentedTimeCode(Field, byte, byte[], DateComponents)},
83   *   {@link #durationFrom(FieldAbsoluteDate)}, {@link #compareTo(FieldAbsoluteDate)}, {@link #equals(Object)}
84   *   and {@link #hashCode()}.</p>
85   *   </li>
86   * </ul>
87   * <p>
88   * A few reference epochs which are commonly used in space systems have been defined. These
89   * epochs can be used as the basis for offset computation. The supported epochs are:
90   * {@link #getJulianEpoch(Field)}, {@link #getModifiedJulianEpoch(Field)}, {@link #getFiftiesEpoch(Field)},
91   * {@link #getCCSDSEpoch(Field)}, {@link #getGalileoEpoch(Field)}, {@link #getGPSEpoch(Field)},
92   * {@link #getJ2000Epoch(Field)}, {@link #getJavaEpoch(Field)}. There are also two factory methods
93   * {@link #createJulianEpoch(CalculusFieldElement)} and {@link #createBesselianEpoch(CalculusFieldElement)}
94   * that can be used to compute other reference epochs like J1900.0 or B1950.0.
95   * In addition to these reference epochs, two other constants are defined for convenience:
96   * {@link #getPastInfinity(Field)} and {@link #getFutureInfinity(Field)}, which can be used either
97   * as dummy dates when a date is not yet initialized, or for initialization of loops searching for
98   * a min or max date.
99   * </p>
100  * <p>
101  * Instances of the <code>FieldAbsoluteDate&lt;T&gt;</code> class are guaranteed to be immutable.
102  * </p>
103  * @author Luc Maisonobe
104  * @see TimeScale
105  * @see TimeStamped
106  * @see ChronologicalComparator
107  * @param <T> type of the field elements
108  */
109 public class FieldAbsoluteDate<T extends CalculusFieldElement<T>>
110         implements FieldTimeStamped<T>, FieldTimeShiftable<FieldAbsoluteDate<T>, T>, Comparable<FieldAbsoluteDate<T>> {
111 
112     /** Reference epoch in seconds from 2000-01-01T12:00:00 TAI.
113      * <p>Beware, it is not {@link #getJ2000Epoch(Field)} since it is in TAI and not in TT.</p> */
114     private final long epoch;
115 
116     /** Offset from the reference epoch in seconds. */
117     private final  T offset;
118 
119     /** Field used by default.*/
120     private final Field<T> field;
121 
122     /** Build an instance from an AbsoluteDate.
123      * @param field used by default
124      * @param date AbsoluteDate to instantiate as a FieldAbsoluteDate
125      */
126     public FieldAbsoluteDate(final Field<T> field, final AbsoluteDate date) {
127         this.field  = field;
128         this.epoch  = date.getEpoch();
129         this.offset = field.getZero().add(date.getOffset());
130     }
131 
132     /** Create an instance with a default value ({@link #getJ2000Epoch(Field)}).
133      *
134      * <p>This method uses the {@link DataContext#getDefault() default data context}.
135      *
136      * @param field field used by default
137      * @see #FieldAbsoluteDate(Field, AbsoluteDate)
138      */
139     @DefaultDataContext
140     public FieldAbsoluteDate(final Field<T> field) {
141         final FieldAbsoluteDate<T> j2000 = getJ2000Epoch(field);
142         this.field  = j2000.field;
143         this.epoch  = j2000.epoch;
144         this.offset = j2000.offset;
145     }
146 
147     /** Build an instance from an elapsed duration since to another instant.
148      * <p>It is important to note that the elapsed duration is <em>not</em>
149      * the difference between two readings on a time scale. As an example,
150      * the duration between the two instants leading to the readings
151      * 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the {@link UTCScale UTC}
152      * time scale is <em>not</em> 1 second, but a stop watch would have measured
153      * an elapsed duration of 2 seconds between these two instances because a leap
154      * second was introduced at the end of 2005 in this time scale.</p>
155      * <p>This constructor is the reverse of the {@link #durationFrom(FieldAbsoluteDate)}
156      * method.</p>
157      * @param since start instant of the measured duration
158      * @param elapsedDuration physically elapsed duration from the <code>since</code>
159      * instant, as measured in a regular time scale
160      * @see #durationFrom(FieldAbsoluteDate)
161      */
162     public FieldAbsoluteDate(final FieldAbsoluteDate<T> since, final T elapsedDuration) {
163         this.field = since.field;
164         // Use 2Sum for high precision.
165         final FieldSumAndResidual<T> sumAndResidual = MathUtils.twoSum(since.offset, elapsedDuration);
166         if (Double.isInfinite(sumAndResidual.getSum().getReal())) {
167             offset = sumAndResidual.getSum();
168             epoch = (sumAndResidual.getSum().getReal() < 0) ? Long.MIN_VALUE : Long.MAX_VALUE;
169         } else {
170             final long dl = (long) FastMath.floor(sumAndResidual.getSum().getReal());
171             final T regularOffset = sumAndResidual.getSum().subtract(dl).add(sumAndResidual.getResidual());
172             if (regularOffset.getReal() >= 0) {
173                 // regular case, the offset is between 0.0 and 1.0
174                 offset = regularOffset;
175                 epoch = since.epoch + dl;
176             } else {
177                 // very rare case, the offset is just before a whole second
178                 // we will loose some bits of accuracy when adding 1 second
179                 // but this will ensure the offset remains in the [0.0; 1.0] interval
180                 offset = regularOffset.add(1.0);
181                 epoch  = since.epoch + dl - 1;
182             }
183         }
184     }
185 
186     /** Build an instance from a location (parsed from a string) in a {@link TimeScale time scale}.
187      * <p>
188      * The supported formats for location are mainly the ones defined in ISO-8601 standard,
189      * the exact subset is explained in {@link DateTimeComponents#parseDateTime(String)},
190      * {@link DateComponents#parseDate(String)} and {@link TimeComponents#parseTime(String)}.
191      * </p>
192      * <p>
193      * As CCSDS ASCII calendar segmented time code is a trimmed down version of ISO-8601,
194      * it is also supported by this constructor.
195      * </p>
196      * @param field field utilized by default
197      * @param location location in the time scale, must be in a supported format
198      * @param timeScale time scale
199      * @exception IllegalArgumentException if location string is not in a supported format
200      */
201     public FieldAbsoluteDate(final Field<T> field, final String location, final TimeScale timeScale) {
202         this(field, DateTimeComponents.parseDateTime(location), timeScale);
203     }
204 
205     /** Build an instance from a location in a {@link TimeScale time scale}.
206      * @param field field utilized by default
207      * @param location location in the time scale
208      * @param timeScale time scale
209      */
210     public FieldAbsoluteDate(final Field<T> field, final DateTimeComponents location, final TimeScale timeScale) {
211         this(field, location.getDate(), location.getTime(), timeScale);
212     }
213 
214     /** Build an instance from a location in a {@link TimeScale time scale}.
215      * @param field field utilized by default
216      * @param date date location in the time scale
217      * @param time time location in the time scale
218      * @param timeScale time scale
219      */
220     public FieldAbsoluteDate(final Field<T> field, final DateComponents date, final TimeComponents time,
221                              final TimeScale timeScale) {
222         final double seconds  = time.getSecond();
223         final double tsOffset = timeScale.offsetToTAI(date, time);
224 
225         // Use 2Sum for high precision.
226         final SumAndResidual sumAndResidual = MathUtils.twoSum(seconds, tsOffset);
227         final long dl = (long) FastMath.floor(sumAndResidual.getSum());
228         final T regularOffset = field.getZero().add((sumAndResidual.getSum() - dl) + sumAndResidual.getResidual());
229         if (regularOffset.getReal() >= 0) {
230             // regular case, the offset is between 0.0 and 1.0
231             offset = regularOffset;
232             epoch  = 60L * ((date.getJ2000Day() * 24L + time.getHour()) * 60L +
233                             time.getMinute() - time.getMinutesFromUTC() - 720L) + dl;
234         } else {
235             // very rare case, the offset is just before a whole second
236             // we will loose some bits of accuracy when adding 1 second
237             // but this will ensure the offset remains in the [0.0; 1.0] interval
238             offset = regularOffset.add(1.0);
239             epoch  = 60L * ((date.getJ2000Day() * 24L + time.getHour()) * 60L +
240                             time.getMinute() - time.getMinutesFromUTC() - 720L) + dl - 1;
241         }
242         this.field = field;
243 
244     }
245 
246     /** Build an instance from a location in a {@link TimeScale time scale}.
247      * @param field field utilized by default
248      * @param year year number (may be 0 or negative for BC years)
249      * @param month month number from 1 to 12
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 FieldAbsoluteDate(final Field<T> field, final int year, final int month, final int day,
259                              final int hour, final int minute, final double second,
260                              final TimeScale timeScale) throws IllegalArgumentException {
261         this(field, 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      * @param field field utilized by default
266      * @param year year number (may be 0 or negative for BC years)
267      * @param month month enumerate
268      * @param day day number from 1 to 31
269      * @param hour hour number from 0 to 23
270      * @param minute minute number from 0 to 59
271      * @param second second number from 0.0 to 60.0 (excluded)
272      * @param timeScale time scale
273      * @exception IllegalArgumentException if inconsistent arguments
274      * are given (parameters out of range)
275      */
276     public FieldAbsoluteDate(final Field<T> field, final int year, final Month month, final int day,
277                              final int hour, final int minute, final double second,
278                              final TimeScale timeScale) throws IllegalArgumentException {
279         this(field, new DateComponents(year, month, day), new TimeComponents(hour, minute, second), timeScale);
280     }
281 
282     /** Build an instance from a location in a {@link TimeScale time scale}.
283      * <p>The hour is set to 00:00:00.000.</p>
284      * @param field field utilized by default
285      * @param date date location in the time scale
286      * @param timeScale time scale
287      * @exception IllegalArgumentException if inconsistent arguments
288      * are given (parameters out of range)
289      */
290     public FieldAbsoluteDate(final Field<T> field, final DateComponents date, final TimeScale timeScale)
291                     throws IllegalArgumentException {
292         this(field, date, TimeComponents.H00, timeScale);
293     }
294 
295     /** Build an instance from a location in a {@link TimeScale time scale}.
296      * <p>The hour is set to 00:00:00.000.</p>
297      * @param field field utilized by default
298      * @param year year number (may be 0 or negative for BC years)
299      * @param month month number from 1 to 12
300      * @param day day number from 1 to 31
301      * @param timeScale time scale
302      * @exception IllegalArgumentException if inconsistent arguments
303      * are given (parameters out of range)
304      */
305     public FieldAbsoluteDate(final Field<T> field, final int year, final int month, final int day,
306                              final TimeScale timeScale) throws IllegalArgumentException {
307         this(field, new DateComponents(year, month, day), TimeComponents.H00, timeScale);
308     }
309 
310     /** Build an instance from a location in a {@link TimeScale time scale}.
311      * <p>The hour is set to 00:00:00.000.</p>
312      * @param field field utilized by default
313      * @param year year number (may be 0 or negative for BC years)
314      * @param month month enumerate
315      * @param day day number from 1 to 31
316      * @param timeScale time scale
317      * @exception IllegalArgumentException if inconsistent arguments
318      * are given (parameters out of range)
319      */
320     public FieldAbsoluteDate(final Field<T> field, final int year, final Month month, final int day,
321                              final TimeScale timeScale) throws IllegalArgumentException {
322         this(field, new DateComponents(year, month, day), TimeComponents.H00, timeScale);
323     }
324 
325     /** Build an instance from a location in a {@link TimeScale time scale}.
326      * @param field field utilized as default
327      * @param location location in the time scale
328      * @param timeScale time scale
329      */
330     public FieldAbsoluteDate(final Field<T> field, final Date location, final TimeScale timeScale) {
331         this(field, new DateComponents(DateComponents.JAVA_EPOCH,
332                                        (int) (location.getTime() / 86400000L)),
333              new TimeComponents(0.001 * (location.getTime() % 86400000L)),
334              timeScale);
335     }
336 
337     /** Build an instance from an {@link Instant instant} in a {@link TimeScale time scale}.
338      * @param field field utilized as default
339      * @param instant instant in the time scale
340      * @param timeScale time scale
341      * @since 12.0
342      */
343     public FieldAbsoluteDate(final Field<T> field, final Instant instant, final TimeScale timeScale) {
344         this(field, new DateComponents(DateComponents.JAVA_EPOCH,
345                                        (int) (instant.getEpochSecond() / 86400L)),
346              instantToTimeComponents(instant),
347              timeScale);
348     }
349 
350     /** Build an instance from an {@link Instant instant} in utc time scale.
351      * @param field field utilized as default
352      * @param instant instant in the utc timescale
353      * @since 12.1
354      */
355     @DefaultDataContext
356     public FieldAbsoluteDate(final Field<T> field, final Instant instant) {
357         this(field, instant, TimeScalesFactory.getUTC());
358     }
359 
360     /** Build an instance from an {@link Instant instant} in the {@link UTCScale time scale}.
361      * @param field field utilized as default
362      * @param instant instant in the time scale
363      * @param utcScale utc time scale
364      * @since 12.1
365      */
366     public FieldAbsoluteDate(final Field<T> field, final Instant instant, final UTCScale utcScale) {
367         this(field, new DateComponents(DateComponents.JAVA_EPOCH,
368                 (int) (instant.getEpochSecond() / 86400l)),
369             instantToTimeComponents(instant),
370             utcScale);
371     }
372 
373     /** Build an instance from an elapsed duration since to another instant.
374      * <p>It is important to note that the elapsed duration is <em>not</em>
375      * the difference between two readings on a time scale.
376      * @param since start instant of the measured duration
377      * @param elapsedDuration physically elapsed duration from the <code>since</code>
378      * instant, as measured in a regular time scale
379      */
380     public FieldAbsoluteDate(final FieldAbsoluteDate<T> since, final double elapsedDuration) {
381         this(since.epoch, elapsedDuration, since.offset);
382     }
383 
384     /** Build an instance from an elapsed duration since to another instant.
385      * <p>It is important to note that the elapsed duration is <em>not</em>
386      * the difference between two readings on a time scale.
387      * @param since start instant of the measured duration
388      * @param elapsedDuration physically elapsed duration from the <code>since</code>
389      * instant, as measured in a regular time scale
390      * @param timeUnit {@link TimeUnit} of the elapsed duration
391      * @since 12.1
392      */
393     public FieldAbsoluteDate(final FieldAbsoluteDate<T> since, final long elapsedDuration, final TimeUnit timeUnit) {
394         this(since.epoch, elapsedDuration, timeUnit, since.offset);
395     }
396 
397 
398     /** Build an instance from an elapsed duration since to another instant.
399      * <p>It is important to note that the elapsed duration is <em>not</em>
400      * the difference between two readings on a time scale.
401      * @param since start instant of the measured duration
402      * @param elapsedDuration physically elapsed duration from the <code>since</code>
403      * instant, as measured in a regular time scale
404      */
405     public FieldAbsoluteDate(final AbsoluteDate since, final T elapsedDuration) {
406         this(since.getEpoch(), since.getOffset(), elapsedDuration);
407     }
408 
409     /** Build an instance from an elapsed duration since to another instant.
410      * <p>It is important to note that the elapsed duration is <em>not</em>
411      * the difference between two readings on a time scale.
412      * @param since start instant of the measured duration
413      * @param elapsedDuration physically elapsed duration from the <code>since</code>
414      * instant, as measured in a regular time scale
415      * @param timeUnit {@link TimeUnit} of the elapsed duration
416      * @param field field utilized by default
417      * @since 12.1
418      */
419     public FieldAbsoluteDate(final AbsoluteDate since,  final long elapsedDuration, final TimeUnit timeUnit, final Field<T> field) {
420         this.field = field;
421 
422         final long elapsedDurationNanoseconds = TimeUnit.NANOSECONDS.convert(elapsedDuration, timeUnit);
423         final long deltaEpoch = elapsedDurationNanoseconds / TimeUnit.SECONDS.toNanos(1);
424         final double deltaOffset = (elapsedDurationNanoseconds - (deltaEpoch * TimeUnit.SECONDS.toNanos(1))) / (double) TimeUnit.SECONDS.toNanos(1);
425         final T newOffset = field.getZero().add(since.getOffset()).add(deltaOffset);
426 
427         if (newOffset.getReal() >= 1.0) {
428             // newOffset is in [1.0, 2.0]
429             this.epoch = since.getEpoch() + deltaEpoch + 1L;
430             this.offset = newOffset.subtract(1.0);
431         } else if (newOffset.getReal() < 0) {
432             this.epoch = since.getEpoch() + deltaEpoch - 1L;
433             this.offset = newOffset.add(1.0);
434         } else {
435             this.epoch = since.getEpoch() + deltaEpoch;
436             this.offset = newOffset;
437         }
438     }
439 
440     /** Build an instance from an apparent clock offset with respect to another
441      * instant <em>in the perspective of a specific {@link TimeScale time scale}</em>.
442      * <p>It is important to note that the apparent clock offset <em>is</em> the
443      * difference between two readings on a time scale and <em>not</em> an elapsed
444      * duration. As an example, the apparent clock offset between the two instants
445      * leading to the readings 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the
446      * {@link UTCScale UTC} time scale is 1 second, but the elapsed duration is 2
447      * seconds because a leap second has been introduced at the end of 2005 in this
448      * time scale.</p>
449      * <p>This constructor is the reverse of the {@link #offsetFrom(FieldAbsoluteDate,
450      * TimeScale)} method.</p>
451      * @param reference reference instant
452      * @param apparentOffset apparent clock offset from the reference instant
453      * (difference between two readings in the specified time scale)
454      * @param timeScale time scale with respect to which the offset is defined
455      * @see #offsetFrom(FieldAbsoluteDate, TimeScale)
456      */
457     public FieldAbsoluteDate(final FieldAbsoluteDate<T> reference, final double apparentOffset, final TimeScale timeScale) {
458         this(reference.field, new DateTimeComponents(reference.getComponents(timeScale), apparentOffset),
459              timeScale);
460     }
461 
462     /** Build an instance from mixed double and field raw components.
463      * @param epoch reference epoch in seconds from 2000-01-01T12:00:00 TAI
464      * @param tA double part of offset since reference epoch
465      * @param tB field part of offset since reference epoch
466      * @since 9.3
467      */
468     private FieldAbsoluteDate(final long epoch, final double tA, final T tB) {
469         this.field = tB.getField();
470         // Use 2Sum for high precision.
471         final FieldSumAndResidual<T> sumAndResidual = MathUtils.twoSum(field.getZero().add(tA), tB);
472         if (Double.isInfinite(sumAndResidual.getSum().getReal())) {
473             this.offset = sumAndResidual.getSum();
474             this.epoch  = (sumAndResidual.getSum().getReal() < 0) ? Long.MIN_VALUE : Long.MAX_VALUE;
475         } else {
476             final long dl = (long) FastMath.floor(sumAndResidual.getSum().getReal());
477             final T regularOffset = sumAndResidual.getSum().subtract(dl).add(sumAndResidual.getResidual());
478             if (regularOffset.getReal() >= 0) {
479                 // regular case, the offset is between 0.0 and 1.0
480                 this.offset = regularOffset;
481                 this.epoch  = epoch + dl;
482             } else {
483                 // very rare case, the offset is just before a whole second
484                 // we will lose some bits of accuracy when adding 1 second
485                 // but this will ensure the offset remains in the [0.0; 1.0) interval
486                 this.offset = regularOffset.add(1.0);
487                 this.epoch  = epoch + dl - 1;
488             }
489         }
490     }
491 
492     /** Build an instance from mixed double and field raw components.
493      * @param epoch reference epoch in seconds from 2000-01-01T12:00:00 TAI
494      * @param tA numeric part of offset since reference epoch
495      * @param tATimeUnit {@link TimeUnit} for tA
496      * @param tB field part of offset since reference epoch
497      * @since 12.1
498      */
499     private FieldAbsoluteDate(final long epoch, final long tA, final TimeUnit tATimeUnit, final T tB) {
500         this.field = tB.getField();
501 
502         final long elapsedDurationNanoseconds = TimeUnit.NANOSECONDS.convert(tA, tATimeUnit);
503         final long deltaEpoch = elapsedDurationNanoseconds / TimeUnit.SECONDS.toNanos(1);
504         final double deltaOffset = (elapsedDurationNanoseconds - (deltaEpoch * TimeUnit.SECONDS.toNanos(1))) / (double) TimeUnit.SECONDS.toNanos(1);
505         final T newOffset = field.getZero().add(tB).add(deltaOffset);
506 
507         if (newOffset.getReal() >= 1.0) {
508             // newOffset is in [1.0, 2.0]
509             this.epoch = epoch + deltaEpoch + 1L;
510             offset = newOffset.subtract(1.0);
511         } else if (newOffset.getReal() < 0) {
512             this.epoch = epoch + deltaEpoch - 1L;
513             offset = newOffset.add(1.0);
514         } else {
515             this.epoch = epoch + deltaEpoch;
516             offset = newOffset;
517         }
518     }
519 
520     /** Extract time components from an instant within the day.
521      * @param instant instant to extract the number of seconds within the day
522      * @return time components
523      */
524     private static TimeComponents instantToTimeComponents(final Instant instant) {
525         final int secInDay = (int) (instant.getEpochSecond() % 86400L);
526         return new TimeComponents(secInDay, 1.0e-9 * instant.getNano());
527     }
528 
529     /** Build an instance from a CCSDS Unsegmented Time Code (CUC).
530      * <p>
531      * CCSDS Unsegmented Time Code is defined in the blue book:
532      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
533      * </p>
534      * <p>
535      * If the date to be parsed is formatted using version 3 of the standard
536      * (CCSDS 301.0-B-3 published in 2002) or if the extension of the preamble
537      * field introduced in version 4 of the standard is not used, then the
538      * {@code preambleField2} parameter can be set to 0.
539      * </p>
540      *
541      * <p>This method uses the {@link DataContext#getDefault() default data context} if
542      * the CCSDS epoch is used.
543      *
544      * @param field field for the components
545      * @param preambleField1 first byte of the field specifying the format, often
546      * not transmitted in data interfaces, as it is constant for a given data interface
547      * @param preambleField2 second byte of the field specifying the format
548      * (added in revision 4 of the CCSDS standard in 2010), often not transmitted in data
549      * interfaces, as it is constant for a given data interface (value ignored if presence
550      * not signaled in {@code preambleField1})
551      * @param timeField byte array containing the time code
552      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
553      * specifies the {@link #getCCSDSEpoch(Field) CCSDS reference epoch} is used (and hence
554      * may be null in this case)
555      * @return an instance corresponding to the specified date
556      * @param <T> the type of the field elements
557      * @see #parseCCSDSUnsegmentedTimeCode(Field, byte, byte, byte[], FieldAbsoluteDate,
558      * FieldAbsoluteDate)
559      */
560     @DefaultDataContext
561     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> parseCCSDSUnsegmentedTimeCode(final Field<T> field,
562                                                                                                          final byte preambleField1,
563                                                                                                          final byte preambleField2,
564                                                                                                          final byte[] timeField,
565                                                                                                          final FieldAbsoluteDate<T> agencyDefinedEpoch) {
566         return parseCCSDSUnsegmentedTimeCode(field, preambleField1, preambleField2,
567                                              timeField, agencyDefinedEpoch,
568                                              new FieldAbsoluteDate<>(
569                                                              field,
570                                                              DataContext.getDefault().getTimeScales().getCcsdsEpoch()));
571     }
572 
573     /**
574      * Build an instance from a CCSDS Unsegmented Time Code (CUC).
575      * <p>
576      * CCSDS Unsegmented Time Code is defined in the blue book: CCSDS Time Code Format
577      * (CCSDS 301.0-B-4) published in November 2010
578      * </p>
579      * <p>
580      * If the date to be parsed is formatted using version 3 of the standard (CCSDS
581      * 301.0-B-3 published in 2002) or if the extension of the preamble field introduced
582      * in version 4 of the standard is not used, then the {@code preambleField2} parameter
583      * can be set to 0.
584      * </p>
585      *
586      * @param <T>                the type of the field elements
587      * @param field              field for the components
588      * @param preambleField1     first byte of the field specifying the format, often not
589      *                           transmitted in data interfaces, as it is constant for a
590      *                           given data interface
591      * @param preambleField2     second byte of the field specifying the format (added in
592      *                           revision 4 of the CCSDS standard in 2010), often not
593      *                           transmitted in data interfaces, as it is constant for a
594      *                           given data interface (value ignored if presence not
595      *                           signaled in {@code preambleField1})
596      * @param timeField          byte array containing the time code
597      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field specifies
598      *                           the CCSDS reference epoch is used (and hence may be null
599      *                           in this case)
600      * @param ccsdsEpoch         reference epoch, ignored if the preamble field specifies
601      *                           the agency epoch is used.
602      * @return an instance corresponding to the specified date
603      * @since 10.1
604      */
605     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> parseCCSDSUnsegmentedTimeCode(final Field<T> field,
606                                                                                                          final byte preambleField1,
607                                                                                                          final byte preambleField2,
608                                                                                                          final byte[] timeField,
609                                                                                                          final FieldAbsoluteDate<T> agencyDefinedEpoch,
610                                                                                                          final FieldAbsoluteDate<T> ccsdsEpoch) {
611         final CcsdsUnsegmentedTimeCode<FieldAbsoluteDate<T>> timeCode =
612             new CcsdsUnsegmentedTimeCode<>(preambleField1, preambleField2, timeField,
613                                            agencyDefinedEpoch, ccsdsEpoch);
614         return new FieldAbsoluteDate<>(timeCode.getEpoch(), timeCode.getSeconds()).
615                shiftedBy(timeCode.getSubSecond());
616     }
617 
618     /** Build an instance from a CCSDS Day Segmented Time Code (CDS).
619      * <p>
620      * CCSDS Day Segmented Time Code is defined in the blue book:
621      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
622      * </p>
623      *
624      * <p>This method uses the {@link DataContext#getDefault() default data context}.
625      *
626      * @param field field for the components
627      * @param preambleField field specifying the format, often not transmitted in
628      * data interfaces, as it is constant for a given data interface
629      * @param timeField byte array containing the time code
630      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
631      * specifies the {@link #getCCSDSEpoch(Field) CCSDS reference epoch} is used (and hence
632      * may be null in this case)
633      * @return an instance corresponding to the specified date
634      * @param <T> the type of the field elements
635      * @see #parseCCSDSDaySegmentedTimeCode(Field, byte, byte[], DateComponents,
636      * TimeScale)
637      */
638     @DefaultDataContext
639     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> parseCCSDSDaySegmentedTimeCode(final Field<T> field,
640                                                                                                           final byte preambleField, final byte[] timeField,
641                                                                                                           final DateComponents agencyDefinedEpoch) {
642         return parseCCSDSDaySegmentedTimeCode(field, preambleField, timeField,
643                                               agencyDefinedEpoch, DataContext.getDefault().getTimeScales().getUTC());
644     }
645 
646     /**
647      * Build an instance from a CCSDS Day Segmented Time Code (CDS).
648      * <p>
649      * CCSDS Day Segmented Time Code is defined in the blue book: CCSDS Time Code Format
650      * (CCSDS 301.0-B-4) published in November 2010
651      * </p>
652      *
653      * @param <T>                the type of the field elements
654      * @param field              field for the components
655      * @param preambleField      field specifying the format, often not transmitted in
656      *                           data interfaces, as it is constant for a given data
657      *                           interface
658      * @param timeField          byte array containing the time code
659      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field specifies
660      *                           the {@link #getCCSDSEpoch(Field) CCSDS reference epoch}
661      *                           is used (and hence may be null in this case)
662      * @param utc                time scale used to compute date and time components.
663      * @return an instance corresponding to the specified date
664      * @since 10.1
665      */
666     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> parseCCSDSDaySegmentedTimeCode(final Field<T> field,
667                                                                                                           final byte preambleField,
668                                                                                                           final byte[] timeField,
669                                                                                                           final DateComponents agencyDefinedEpoch,
670                                                                                                           final TimeScale utc) {
671 
672         final CcsdsSegmentedTimeCode timeCode = new CcsdsSegmentedTimeCode(preambleField, timeField,
673                                                                            agencyDefinedEpoch);
674         return new FieldAbsoluteDate<>(field, timeCode.getDate(), timeCode.getTime(), utc).
675                shiftedBy(timeCode.getSubSecond());
676     }
677 
678     /** Build an instance from a CCSDS Calendar Segmented Time Code (CCS).
679      * <p>
680      * CCSDS Calendar Segmented Time Code is defined in the blue book:
681      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
682      * </p>
683      *
684      * <p>This method uses the {@link DataContext#getDefault() default data context}.
685      *
686      * @param preambleField field specifying the format, often not transmitted in
687      * data interfaces, as it is constant for a given data interface
688      * @param timeField byte array containing the time code
689      * @return an instance corresponding to the specified date
690      * @see #parseCCSDSCalendarSegmentedTimeCode(byte, byte[], TimeScale)
691      */
692     @DefaultDataContext
693     public FieldAbsoluteDate<T> parseCCSDSCalendarSegmentedTimeCode(final byte preambleField, final byte[] timeField) {
694         return parseCCSDSCalendarSegmentedTimeCode(preambleField, timeField,
695                                                    DataContext.getDefault().getTimeScales().getUTC());
696     }
697 
698     /**
699      * Build an instance from a CCSDS Calendar Segmented Time Code (CCS).
700      * <p>
701      * CCSDS Calendar Segmented Time Code is defined in the blue book: CCSDS Time Code
702      * Format (CCSDS 301.0-B-4) published in November 2010
703      * </p>
704      *
705      * @param preambleField field specifying the format, often not transmitted in data
706      *                      interfaces, as it is constant for a given data interface
707      * @param timeField     byte array containing the time code
708      * @param utc           time scale used to compute date and time components.
709      * @return an instance corresponding to the specified date
710      * @since 10.1
711      */
712     public FieldAbsoluteDate<T> parseCCSDSCalendarSegmentedTimeCode(final byte preambleField,
713                                                                     final byte[] timeField,
714                                                                     final TimeScale utc) {
715         final CcsdsSegmentedTimeCode timeCode = new CcsdsSegmentedTimeCode(preambleField, timeField);
716         return new FieldAbsoluteDate<>(field, timeCode.getDate(), timeCode.getTime(), utc).
717                shiftedBy(timeCode.getSubSecond());
718     }
719 
720     /** Build an instance corresponding to a Julian Day date.
721      * @param jd Julian day
722      * @param secondsSinceNoon seconds in the Julian day
723      * (BEWARE, Julian days start at noon, so 0.0 is noon)
724      * @param timeScale time scale in which the seconds in day are defined
725      * @return a new instant
726      * @param <T> the type of the field elements
727      */
728     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createJDDate(final int jd, final T secondsSinceNoon,
729                                                                                         final TimeScale timeScale) {
730         return new FieldAbsoluteDate<>(secondsSinceNoon.getField(), new DateComponents(DateComponents.JULIAN_EPOCH, jd),
731                         TimeComponents.H12, timeScale).shiftedBy(secondsSinceNoon);
732     }
733 
734     /** Build an instance corresponding to a Julian Day date.
735      * <p>
736      * This function should be preferred to {@link #createJDDate(int, CalculusFieldElement, TimeScale)} when the target time scale
737      * has a non-constant offset with respect to TAI.
738      * <p>
739      * The idea is to introduce a pivot time scale that is close to the target time scale but has a constant bias with TAI.
740      * <p>
741      * For example, to get a date from an MJD in TDB time scale, it's advised to use the TT time scale
742      * as a pivot scale. TT is very close to TDB and has constant offset to TAI.
743      * </p>
744      * @param jd Julian day
745      * @param secondsSinceNoon seconds in the Julian day
746      * (BEWARE, Julian days start at noon, so 0.0 is noon)
747      * @param timeScale time scale in which the seconds in day are defined
748      * @param pivotTimeScale pivot timescale used as intermediate timescale
749      * @return a new instant
750      * @param <T> the type of the field elements
751      */
752     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createJDDate(final int jd, final T secondsSinceNoon,
753                                                                                         final TimeScale timeScale,
754                                                                                         final TimeScale pivotTimeScale) {
755         // Get the date in pivot timescale
756         final FieldAbsoluteDate<T> dateInPivotTimeScale = createJDDate(jd, secondsSinceNoon, pivotTimeScale);
757 
758         // Compare offsets to TAI of the two time scales
759         final T offsetFromTAI = timeScale.offsetFromTAI(dateInPivotTimeScale).
760                 subtract(pivotTimeScale.offsetFromTAI(dateInPivotTimeScale));
761 
762         // Return date in desired timescale
763         return dateInPivotTimeScale.shiftedBy(offsetFromTAI.multiply(-1.));
764     }
765 
766     /** Build an instance corresponding to a Modified Julian Day date.
767      * @param mjd modified Julian day
768      * @param secondsInDay seconds in the day
769      * @param timeScale time scale in which the seconds in day are defined
770      * @return a new instant
771      * @param <T> the type of the field elements
772      */
773     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createMJDDate(final int mjd, final T secondsInDay,
774                                                                                          final TimeScale timeScale) {
775         return new FieldAbsoluteDate<>(secondsInDay.getField(),
776                         new DateComponents(DateComponents.MODIFIED_JULIAN_EPOCH, mjd),
777                         TimeComponents.H00,
778                         timeScale).shiftedBy(secondsInDay);
779     }
780 
781     /** Build an instance corresponding to a GPS date.
782      *
783      * <p>This method uses the {@link DataContext#getDefault() default data context}.
784      *
785      * <p>GPS dates are provided as a week number starting at
786      * {@link #getGPSEpoch(Field) GPS epoch} and as a number of milliseconds
787      * since week start.</p>
788      * @param weekNumber week number since {@link #getGPSEpoch(Field) GPS epoch}
789      * @param milliInWeek number of milliseconds since week start
790      * @return a new instant
791      * @param <T> the type of the field elements
792      * @see #createGPSDate(int, CalculusFieldElement, TimeScale)
793      */
794     @DefaultDataContext
795     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createGPSDate(final int weekNumber, final T milliInWeek) {
796         return createGPSDate(weekNumber, milliInWeek,
797                              DataContext.getDefault().getTimeScales().getGPS());
798     }
799 
800     /**
801      * Build an instance corresponding to a GPS date.
802      * <p>GPS dates are provided as a week number starting at
803      * {@link #getGPSEpoch(Field) GPS epoch} and as a number of milliseconds since week
804      * start.</p>
805      *
806      * @param <T>         the type of the field elements
807      * @param weekNumber  week number since {@link #getGPSEpoch(Field) GPS epoch}
808      * @param milliInWeek number of milliseconds since week start
809      * @param gps         GPS time scale.
810      * @return a new instant
811      * @since 10.1
812      */
813     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createGPSDate(
814                                                                                          final int weekNumber,
815                                                                                          final T milliInWeek,
816                                                                                          final TimeScale gps) {
817 
818         final int day = (int) FastMath.floor(milliInWeek.getReal() / (1000.0 * Constants.JULIAN_DAY));
819         final T secondsInDay = milliInWeek.divide(1000.0).subtract(day * Constants.JULIAN_DAY);
820         return new FieldAbsoluteDate<>(milliInWeek.getField(), new DateComponents(DateComponents.GPS_EPOCH, weekNumber * 7 + day),
821                         TimeComponents.H00, gps).shiftedBy(secondsInDay);
822     }
823 
824     /** Build an instance corresponding to a Julian Epoch (JE).
825      * <p>According to Lieske paper: <a
826      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
827      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
828      * vol. 73, no. 3, Mar. 1979, p. 282-284, Julian Epoch is related to Julian Ephemeris Date as:
829      * <pre>JE = 2000.0 + (JED - 2451545.0) / 365.25</pre>
830      * <p>This method reverts the formula above and computes an {@code FieldAbsoluteDate<T>} from the Julian Epoch.
831      *
832      * <p>This method uses the {@link DataContext#getDefault() default data context}.
833      *
834      * @param <T> the type of the field elements
835      * @param julianEpoch Julian epoch, like 2000.0 for defining the classical reference J2000.0
836      * @return a new instant
837      * @see #getJ2000Epoch(Field)
838      * @see #createBesselianEpoch(CalculusFieldElement)
839      * @see #createJulianEpoch(CalculusFieldElement, TimeScales)
840      */
841     @DefaultDataContext
842     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createJulianEpoch(final T julianEpoch) {
843         return createJulianEpoch(julianEpoch,
844                                  DataContext.getDefault().getTimeScales());
845     }
846 
847     /**
848      * Build an instance corresponding to a Julian Epoch (JE).
849      * <p>According to Lieske paper: <a
850      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
851      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>,
852      * Astronomy and Astrophysics, vol. 73, no. 3, Mar. 1979, p. 282-284, Julian Epoch is
853      * related to Julian Ephemeris Date as:
854      * <pre>JE = 2000.0 + (JED - 2451545.0) / 365.25</pre>
855      * <p>This method reverts the formula above and computes an {@code
856      * FieldAbsoluteDate<T>} from the Julian Epoch.
857      *
858      * @param <T>         the type of the field elements
859      * @param julianEpoch Julian epoch, like 2000.0 for defining the classical reference
860      *                    J2000.0
861      * @param timeScales  used in the computation.
862      * @return a new instant
863      * @see #getJ2000Epoch(Field)
864      * @see #createBesselianEpoch(CalculusFieldElement)
865      * @see TimeScales#createJulianEpoch(double)
866      * @since 10.1
867      */
868     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createJulianEpoch(
869                                                                                              final T julianEpoch,
870                                                                                              final TimeScales timeScales) {
871 
872         final Field<T> field = julianEpoch.getField();
873         return new FieldAbsoluteDate<>(new FieldAbsoluteDate<>(field, timeScales.getJ2000Epoch()),
874                         julianEpoch.subtract(2000.0).multiply(Constants.JULIAN_YEAR));
875     }
876 
877     /** Build an instance corresponding to a Besselian Epoch (BE).
878      * <p>According to Lieske paper: <a
879      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
880      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
881      * vol. 73, no. 3, Mar. 1979, p. 282-284, Besselian Epoch is related to Julian Ephemeris Date as:</p>
882      * <pre>
883      * BE = 1900.0 + (JED - 2415020.31352) / 365.242198781
884      * </pre>
885      * <p>
886      * This method reverts the formula above and computes an {@code FieldAbsoluteDate<T>} from the Besselian Epoch.
887      * </p>
888      *
889      * <p>This method uses the {@link DataContext#getDefault() default data context}.
890      *
891      * @param <T> the type of the field elements
892      * @param besselianEpoch Besselian epoch, like 1950 for defining the classical reference B1950.0
893      * @return a new instant
894      * @see #createJulianEpoch(CalculusFieldElement)
895      * @see #createBesselianEpoch(CalculusFieldElement, TimeScales)
896      */
897     @DefaultDataContext
898     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createBesselianEpoch(final T besselianEpoch) {
899         return createBesselianEpoch(besselianEpoch,
900                                     DataContext.getDefault().getTimeScales());
901     }
902 
903     /**
904      * Build an instance corresponding to a Besselian Epoch (BE).
905      * <p>According to Lieske paper: <a
906      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
907      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>,
908      * Astronomy and Astrophysics, vol. 73, no. 3, Mar. 1979, p. 282-284, Besselian Epoch
909      * is related to Julian Ephemeris Date as:</p>
910      * <pre>
911      * BE = 1900.0 + (JED - 2415020.31352) / 365.242198781
912      * </pre>
913      * <p>
914      * This method reverts the formula above and computes an {@code FieldAbsoluteDate<T>}
915      * from the Besselian Epoch.
916      * </p>
917      *
918      * @param <T>            the type of the field elements
919      * @param besselianEpoch Besselian epoch, like 1950 for defining the classical
920      *                       reference B1950.0
921      * @param timeScales     used in the computation.
922      * @return a new instant
923      * @see #createJulianEpoch(CalculusFieldElement)
924      * @see TimeScales#createBesselianEpoch(double)
925      * @since 10.1
926      */
927     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> createBesselianEpoch(
928                                                                                                 final T besselianEpoch,
929                                                                                                 final TimeScales timeScales) {
930 
931         final Field<T> field = besselianEpoch.getField();
932         return new FieldAbsoluteDate<>(new FieldAbsoluteDate<>(field, timeScales.getJ2000Epoch()),
933                         besselianEpoch.subtract(1900).multiply(Constants.BESSELIAN_YEAR).add(
934                                                                                              Constants.JULIAN_DAY * (-36525) + Constants.JULIAN_DAY * 0.31352));
935     }
936 
937     /** Reference epoch for julian dates: -4712-01-01T12:00:00 Terrestrial Time.
938      * <p>Both <code>java.util.Date</code> and {@link DateComponents} classes
939      * follow the astronomical conventions and consider a year 0 between
940      * years -1 and +1, hence this reference date lies in year -4712 and not
941      * in year -4713 as can be seen in other documents or programs that obey
942      * a different convention (for example the <code>convcal</code> utility).</p>
943      *
944      * <p>This method uses the {@link DataContext#getDefault() default data context}.
945      *
946      * @param <T> the type of the field elements
947      * @param field field for the components
948      * @return the reference epoch for julian dates as a FieldAbsoluteDate
949      * @see AbsoluteDate#JULIAN_EPOCH
950      * @see TimeScales#getJulianEpoch()
951      */
952     @DefaultDataContext
953     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getJulianEpoch(final Field<T> field) {
954         return new FieldAbsoluteDate<>(field,
955                         DataContext.getDefault().getTimeScales().getJulianEpoch());
956     }
957 
958     /** Reference epoch for modified julian dates: 1858-11-17T00:00:00 Terrestrial Time.
959      *
960      * <p>This method uses the {@link DataContext#getDefault() default data context}.
961      *
962      * @param <T> the type of the field elements
963      * @param field field for the components
964      * @return the reference epoch for modified julian dates as a FieldAbsoluteDate
965      * @see AbsoluteDate#MODIFIED_JULIAN_EPOCH
966      * @see TimeScales#getModifiedJulianEpoch()
967      */
968     @DefaultDataContext
969     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getModifiedJulianEpoch(final Field<T> field) {
970         return new FieldAbsoluteDate<>(field,
971                         DataContext.getDefault().getTimeScales().getModifiedJulianEpoch());
972     }
973 
974     /** Reference epoch for 1950 dates: 1950-01-01T00:00:00 Terrestrial Time.
975      *
976      * <p>This method uses the {@link DataContext#getDefault() default data context}.
977      *
978      * @param <T> the type of the field elements
979      * @param field field for the components
980      * @return the reference epoch for 1950 dates as a FieldAbsoluteDate
981      * @see AbsoluteDate#FIFTIES_EPOCH
982      * @see TimeScales#getFiftiesEpoch()
983      */
984     @DefaultDataContext
985     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getFiftiesEpoch(final Field<T> field) {
986         return new FieldAbsoluteDate<>(field,
987                         DataContext.getDefault().getTimeScales().getFiftiesEpoch());
988     }
989 
990     /** Reference epoch for CCSDS Time Code Format (CCSDS 301.0-B-4).
991      * <p>
992      * This method uses the {@link DataContext#getDefault() default data context}.
993      * </p>
994      * 1958-01-01T00:00:00 International Atomic Time (<em>not</em> UTC).
995      * @param <T> the type of the field elements
996      * @param field field for the components
997      * @return the reference epoch for CCSDS Time Code Format as a FieldAbsoluteDate
998      * @see AbsoluteDate#CCSDS_EPOCH
999      * @see TimeScales#getCcsdsEpoch()
1000      */
1001     @DefaultDataContext
1002     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getCCSDSEpoch(final Field<T> field) {
1003         return new FieldAbsoluteDate<>(field,
1004                         DataContext.getDefault().getTimeScales().getCcsdsEpoch());
1005     }
1006 
1007     /** Reference epoch for Galileo System Time: 1999-08-22T00:00:00 UTC.
1008      *
1009      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1010      *
1011      * @param <T> the type of the field elements
1012      * @param field field for the components
1013      * @return the reference epoch for Galileo System Time as a FieldAbsoluteDate
1014      * @see AbsoluteDate#GALILEO_EPOCH
1015      * @see TimeScales#getGalileoEpoch()
1016      */
1017     @DefaultDataContext
1018     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getGalileoEpoch(final Field<T> field) {
1019         return new FieldAbsoluteDate<>(field,
1020                         DataContext.getDefault().getTimeScales().getGalileoEpoch());
1021     }
1022 
1023     /** Reference epoch for GPS weeks: 1980-01-06T00:00:00 GPS time.
1024      *
1025      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1026      *
1027      * @param <T> the type of the field elements
1028      * @param field field for the components
1029      * @return the reference epoch for GPS weeks as a FieldAbsoluteDate
1030      * @see AbsoluteDate#GPS_EPOCH
1031      * @see TimeScales#getGpsEpoch()
1032      */
1033     @DefaultDataContext
1034     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getGPSEpoch(final Field<T> field) {
1035         return new FieldAbsoluteDate<>(field,
1036                         DataContext.getDefault().getTimeScales().getGpsEpoch());
1037     }
1038 
1039     /** J2000.0 Reference epoch: 2000-01-01T12:00:00 Terrestrial Time (<em>not</em> UTC).
1040      *
1041      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1042      *
1043      * @param <T> the type of the field elements
1044      * @param field field for the components
1045      * @return the J2000.0 reference epoch as a FieldAbsoluteDate
1046      * @see #createJulianEpoch(CalculusFieldElement)
1047      * @see AbsoluteDate#J2000_EPOCH
1048      * @see TimeScales#getJ2000Epoch()
1049      */
1050     @DefaultDataContext
1051     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getJ2000Epoch(final Field<T> field) {
1052         return new FieldAbsoluteDate<>(field,
1053                         DataContext.getDefault().getTimeScales().getJ2000Epoch());
1054     }
1055 
1056     /** Java Reference epoch: 1970-01-01T00:00:00 Universal Time Coordinate.
1057      *
1058      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1059      *
1060      * <p>
1061      * Between 1968-02-01 and 1972-01-01, UTC-TAI = 4.213 170 0s + (MJD - 39 126) x 0.002 592s.
1062      * As on 1970-01-01 MJD = 40587, UTC-TAI = 8.000082s
1063      * </p>
1064      * @param <T> the type of the field elements
1065      * @param field field for the components
1066      * @return the Java reference epoch as a FieldAbsoluteDate
1067      * @see AbsoluteDate#JAVA_EPOCH
1068      * @see TimeScales#getJavaEpoch()
1069      */
1070     @DefaultDataContext
1071     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getJavaEpoch(final Field<T> field) {
1072         return new FieldAbsoluteDate<>(field,
1073                         DataContext.getDefault().getTimeScales().getJavaEpoch());
1074     }
1075 
1076     /** Dummy date at infinity in the past direction.
1077      * @param <T> the type of the field elements
1078      * @param field field for the components
1079      * @return a dummy date at infinity in the past direction as a FieldAbsoluteDate
1080      * @see AbsoluteDate#PAST_INFINITY
1081      * @see TimeScales#getPastInfinity()
1082      */
1083     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getPastInfinity(final Field<T> field) {
1084         return new FieldAbsoluteDate<>(field, AbsoluteDate.PAST_INFINITY);
1085     }
1086 
1087     /** Dummy date at infinity in the future direction.
1088      * @param <T> the type of the field elements
1089      * @param field field for the components
1090      * @return a dummy date at infinity in the future direction as a FieldAbsoluteDate
1091      * @see AbsoluteDate#FUTURE_INFINITY
1092      * @see TimeScales#getFutureInfinity()
1093      */
1094     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getFutureInfinity(final Field<T> field) {
1095         return new FieldAbsoluteDate<>(field, AbsoluteDate.FUTURE_INFINITY);
1096     }
1097 
1098     /**
1099      * Get an arbitrary date. Useful when a non-null date is needed but its values does
1100      * not matter.
1101      *
1102      * @param <T>   the type of the field elements
1103      * @param field field for the components
1104      * @return an arbitrary date.
1105      */
1106     public static <T extends CalculusFieldElement<T>> FieldAbsoluteDate<T> getArbitraryEpoch(final Field<T> field) {
1107 
1108         return new FieldAbsoluteDate<>(field, AbsoluteDate.ARBITRARY_EPOCH);
1109     }
1110 
1111 
1112     /** Get a time-shifted date.
1113      * <p>
1114      * Calling this method is equivalent to call {@code new FieldAbsoluteDate&lt;&gt;(this, dt)}.
1115      * </p>
1116      * @param dt time shift in seconds
1117      * @return a new date, shifted with respect to instance (which is immutable)
1118      * @see org.orekit.utils.FieldPVCoordinates#shiftedBy(double)
1119      * @see org.orekit.attitudes.FieldAttitude#shiftedBy(double)
1120      * @see org.orekit.orbits.FieldOrbit#shiftedBy(double)
1121      * @see org.orekit.propagation.FieldSpacecraftState#shiftedBy(double)
1122      */
1123     @Override
1124     public FieldAbsoluteDate<T> shiftedBy(final T dt) {
1125         return new FieldAbsoluteDate<>(this, dt);
1126     }
1127 
1128     /** Compute the physically elapsed duration between two instants.
1129      * <p>The returned duration is the number of seconds physically
1130      * elapsed between the two instants, measured in a regular time
1131      * scale with respect to surface of the Earth (i.e either the {@link
1132      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
1133      * GPSScale GPS scale}). It is the only method that gives a
1134      * duration with a physical meaning.</p>
1135      * <p>This method gives the same result (with less computation)
1136      * as calling {@link #offsetFrom(FieldAbsoluteDate, TimeScale)}
1137      * with a second argument set to one of the regular scales cited
1138      * above.</p>
1139      * <p>This method is the reverse of the {@link #FieldAbsoluteDate(FieldAbsoluteDate,
1140      * double)} constructor.</p>
1141      * @param instant instant to subtract from the instance
1142      * @return offset in seconds between the two instants (positive
1143      * if the instance is posterior to the argument)
1144      * @see #offsetFrom(FieldAbsoluteDate, TimeScale)
1145      * @see #FieldAbsoluteDate(FieldAbsoluteDate, double)
1146      */
1147     public T durationFrom(final FieldAbsoluteDate<T> instant) {
1148         return offset.subtract(instant.offset).add(epoch - instant.epoch);
1149     }
1150 
1151     /** Compute the physically elapsed duration between two instants.
1152      * <p>The returned duration is the number of seconds physically
1153      * elapsed between the two instants, measured in a regular time
1154      * scale with respect to surface of the Earth (i.e either the {@link
1155      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
1156      * GPSScale GPS scale}). It is the only method that gives a
1157      * duration with a physical meaning.</p>
1158      * <p>This method gives the same result (with less computation)
1159      * as calling {@link #offsetFrom(FieldAbsoluteDate, TimeScale)}
1160      * with a second argument set to one of the regular scales cited
1161      * above.</p>
1162      * <p>This method is the reverse of the {@link #FieldAbsoluteDate(FieldAbsoluteDate,
1163      * double)} constructor.</p>
1164      * @param instant instant to subtract from the instance
1165      * @param timeUnit {@link TimeUnit} precision for the offset
1166      * @return offset in seconds between the two instants (positive
1167      * if the instance is posterior to the argument)
1168      * @see #offsetFrom(FieldAbsoluteDate, TimeScale)
1169      * @see #FieldAbsoluteDate(FieldAbsoluteDate, double)
1170      */
1171     public T durationFrom(final FieldAbsoluteDate<T> instant, final TimeUnit timeUnit) {
1172         final long deltaEpoch = timeUnit.convert(epoch - instant.epoch, TimeUnit.SECONDS);
1173 
1174         final long multiplier = timeUnit.convert(1, TimeUnit.SECONDS);
1175         final T deltaOffset = offset.getField().getZero().add(offset.subtract(instant.offset).multiply(multiplier).round());
1176 
1177         return deltaOffset.add(deltaEpoch);
1178     }
1179 
1180     /** Compute the physically elapsed duration between two instants.
1181      * <p>The returned duration is the number of seconds physically
1182      * elapsed between the two instants, measured in a regular time
1183      * scale with respect to surface of the Earth (i.e either the {@link
1184      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
1185      * GPSScale GPS scale}). It is the only method that gives a
1186      * duration with a physical meaning.</p>
1187      * <p>This method gives the same result (with less computation)
1188      * as calling {@link #offsetFrom(FieldAbsoluteDate, TimeScale)}
1189      * with a second argument set to one of the regular scales cited
1190      * above.</p>
1191      * <p>This method is the reverse of the {@link #FieldAbsoluteDate(FieldAbsoluteDate,
1192      * double)} constructor.</p>
1193      * @param instant instant to subtract from the instance
1194      * @return offset in seconds between the two instants (positive
1195      * if the instance is posterior to the argument)
1196      * @see #offsetFrom(FieldAbsoluteDate, TimeScale)
1197      * @see #FieldAbsoluteDate(FieldAbsoluteDate, double)
1198      */
1199     public T durationFrom(final AbsoluteDate instant) {
1200         return offset.subtract(instant.getOffset()).add(epoch - instant.getEpoch());
1201     }
1202 
1203     /** Compute the physically elapsed duration between two instants.
1204      * <p>The returned duration is the number of seconds physically
1205      * elapsed between the two instants, measured in a regular time
1206      * scale with respect to surface of the Earth (i.e either the {@link
1207      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
1208      * GPSScale GPS scale}). It is the only method that gives a
1209      * duration with a physical meaning.</p>
1210      * <p>This method gives the same result (with less computation)
1211      * as calling {@link #offsetFrom(FieldAbsoluteDate, TimeScale)}
1212      * with a second argument set to one of the regular scales cited
1213      * above.</p>
1214      * <p>This method is the reverse of the {@link #FieldAbsoluteDate(FieldAbsoluteDate,
1215      * double)} constructor.</p>
1216      * @param instant instant to subtract from the instance
1217      * @param timeUnit {@link TimeUnit} precision for the offset
1218      * @return offset in the given timeunit between the two instants (positive
1219      * if the instance is posterior to the argument), rounded to the nearest integer {@link TimeUnit}
1220      * @see #FieldAbsoluteDate(FieldAbsoluteDate, long, TimeUnit)
1221      * @since 12.1
1222      */
1223     public T durationFrom(final AbsoluteDate instant, final TimeUnit timeUnit) {
1224         final long deltaEpoch = timeUnit.convert(epoch - instant.getEpoch(), TimeUnit.SECONDS);
1225 
1226         final long multiplier = timeUnit.convert(1, TimeUnit.SECONDS);
1227         final T deltaOffset = offset.getField().getZero().add(offset.subtract(instant.getOffset()).multiply(multiplier).round());
1228 
1229         return deltaOffset.add(deltaEpoch);
1230     }
1231 
1232     /** Compute the apparent clock offset between two instant <em>in the
1233      * perspective of a specific {@link TimeScale time scale}</em>.
1234      * <p>The offset is the number of seconds counted in the given
1235      * time scale between the locations of the two instants, with
1236      * all time scale irregularities removed (i.e. considering all
1237      * days are exactly 86400 seconds long). This method will give
1238      * a result that may not have a physical meaning if the time scale
1239      * is irregular. For example since a leap second was introduced at
1240      * the end of 2005, the apparent offset between 2005-12-31T23:59:59
1241      * and 2006-01-01T00:00:00 is 1 second, but the physical duration
1242      * of the corresponding time interval as returned by the {@link
1243      * #durationFrom(FieldAbsoluteDate)} method is 2 seconds.</p>
1244      * <p>This method is the reverse of the {@link #FieldAbsoluteDate(FieldAbsoluteDate,
1245      * double, TimeScale)} constructor.</p>
1246      * @param instant instant to subtract from the instance
1247      * @param timeScale time scale with respect to which the offset should
1248      * be computed
1249      * @return apparent clock offset in seconds between the two instants
1250      * (positive if the instance is posterior to the argument)
1251      * @see #durationFrom(FieldAbsoluteDate)
1252      * @see #FieldAbsoluteDate(FieldAbsoluteDate, double, TimeScale)
1253      */
1254     public T offsetFrom(final FieldAbsoluteDate<T> instant, final TimeScale timeScale) {
1255         final long   elapsedDurationA = epoch - instant.epoch;
1256         final T elapsedDurationB = offset.add(timeScale.offsetFromTAI(this)).
1257                         subtract(instant.offset.add(timeScale.offsetFromTAI(instant)));
1258         return  elapsedDurationB.add(elapsedDurationA);
1259     }
1260 
1261     /** Compute the offset between two time scales at the current instant.
1262      * <p>The offset is defined as <i>l₁-l₂</i>
1263      * where <i>l₁</i> is the location of the instant in
1264      * the <code>scale1</code> time scale and <i>l₂</i> is the
1265      * location of the instant in the <code>scale2</code> time scale.</p>
1266      * @param scale1 first time scale
1267      * @param scale2 second time scale
1268      * @return offset in seconds between the two time scales at the
1269      * current instant
1270      */
1271     public T timeScalesOffset(final TimeScale scale1, final TimeScale scale2) {
1272         return scale1.offsetFromTAI(this).subtract(scale2.offsetFromTAI(this));
1273     }
1274 
1275     /** Convert the instance to a Java {@link java.util.Date Date}.
1276      * <p>Conversion to the Date class induces a loss of precision because
1277      * the Date class does not provide sub-millisecond information. Java Dates
1278      * are considered to be locations in some times scales.</p>
1279      * @param timeScale time scale to use
1280      * @return a {@link java.util.Date Date} instance representing the location
1281      * of the instant in the time scale
1282      */
1283     public Date toDate(final TimeScale timeScale) {
1284         final double time = epoch + (offset.getReal() + timeScale.offsetFromTAI(this).getReal());
1285         return new Date(FastMath.round((time + 10957.5 * 86400.0) * 1000));
1286     }
1287 
1288     /**
1289      * Convert the instance to a Java {@link java.time.Instant Instant}.
1290      * Nanosecond precision is preserved during this conversion
1291      *
1292      * @return a {@link java.time.Instant Instant} instance representing the location
1293      * of the instant in the utc time scale
1294      * @since 12.1
1295      */
1296     @DefaultDataContext
1297     public Instant toInstant() {
1298         return toInstant(TimeScalesFactory.getTimeScales());
1299     }
1300 
1301     /**
1302      * Convert the instance to a Java {@link java.time.Instant Instant}.
1303      * Nanosecond precision is preserved during this conversion
1304      *
1305      * @param timeScales the timescales to use
1306      * @return a {@link java.time.Instant Instant} instance representing the location
1307      * of the instant in the utc time scale
1308      * @since 12.1
1309      */
1310     public Instant toInstant(final TimeScales timeScales) {
1311         final UTCScale utc = timeScales.getUTC();
1312         final String stringWithoutUtcOffset = toStringWithoutUtcOffset(utc, 9);
1313 
1314         final LocalDateTime localDateTime = LocalDateTime.parse(stringWithoutUtcOffset, DateTimeFormatter.ISO_LOCAL_DATE_TIME);
1315         return localDateTime.toInstant(ZoneOffset.UTC);
1316     }
1317 
1318     /** Split the instance into date/time components.
1319      * @param timeScale time scale to use
1320      * @return date/time components
1321      */
1322     public DateTimeComponents getComponents(final TimeScale timeScale) {
1323 
1324         if (Double.isInfinite(offset.getReal())) {
1325             // special handling for past and future infinity
1326             if (offset.getReal() < 0) {
1327                 return new DateTimeComponents(DateComponents.MIN_EPOCH, TimeComponents.H00);
1328             } else {
1329                 return new DateTimeComponents(DateComponents.MAX_EPOCH,
1330                                               new TimeComponents(23, 59, 59.999));
1331             }
1332         }
1333 
1334         // Compute offset from 2000-01-01T00:00:00 in specified time scale.
1335         // Use 2Sum for high accuracy.
1336         final double taiOffset = timeScale.offsetFromTAI(this).getReal();
1337         final SumAndResidual sumAndResidual = MathUtils.twoSum(offset.getReal(), taiOffset);
1338 
1339         // split date and time
1340         final long   carry = (long) FastMath.floor(sumAndResidual.getSum());
1341         double offset2000B = (sumAndResidual.getSum() - carry) + sumAndResidual.getResidual();
1342         long   offset2000A = epoch + carry + 43200L;
1343         if (offset2000B < 0) {
1344             offset2000A -= 1;
1345             offset2000B += 1;
1346         }
1347         long time = offset2000A % 86400L;
1348         if (time < 0L) {
1349             time += 86400L;
1350         }
1351         final int date = (int) ((offset2000A - time) / 86400L);
1352 
1353         // extract calendar elements
1354         final DateComponents dateComponents = new DateComponents(DateComponents.J2000_EPOCH, date);
1355         // extract time element, accounting for leap seconds
1356         final double leap = timeScale.insideLeap(this) ? timeScale.getLeap(this.toAbsoluteDate()) : 0;
1357         final int minuteDuration = timeScale.minuteDuration(this);
1358         final TimeComponents timeComponents = TimeComponents.fromSeconds((int) time, offset2000B, leap, minuteDuration);
1359 
1360         // build the components
1361         return new DateTimeComponents(dateComponents, timeComponents);
1362 
1363     }
1364 
1365     /** Split the instance into date/time components for a local time.
1366      *
1367      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1368      *
1369      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1370      * negative Westward UTC)
1371      * @return date/time components
1372      * @see #getComponents(int, TimeScale)
1373      */
1374     @DefaultDataContext
1375     public DateTimeComponents getComponents(final int minutesFromUTC) {
1376         return getComponents(minutesFromUTC,
1377                              DataContext.getDefault().getTimeScales().getUTC());
1378     }
1379 
1380     /**
1381      * Split the instance into date/time components for a local time.
1382      *
1383      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1384      *                       negative Westward UTC)
1385      * @param utc            time scale used to compute date and time components.
1386      * @return date/time components
1387      * @since 10.1
1388      */
1389     public DateTimeComponents getComponents(final int minutesFromUTC,
1390                                             final TimeScale utc) {
1391 
1392         final DateTimeComponents utcComponents = getComponents(utc);
1393 
1394         // shift the date according to UTC offset, but WITHOUT touching the seconds,
1395         // as they may exceed 60.0 during a leap seconds introduction,
1396         // and we want to preserve these special cases
1397         final double seconds = utcComponents.getTime().getSecond();
1398         int minute = utcComponents.getTime().getMinute() + minutesFromUTC;
1399         final int hourShift;
1400         if (minute < 0) {
1401             hourShift = (minute - 59) / 60;
1402         } else if (minute > 59) {
1403             hourShift = minute / 60;
1404         } else {
1405             hourShift = 0;
1406         }
1407         minute -= 60 * hourShift;
1408         int hour = utcComponents.getTime().getHour() + hourShift;
1409         final int dayShift;
1410         if (hour < 0) {
1411             dayShift = (hour - 23) / 24;
1412         } else if (hour > 23) {
1413             dayShift = hour / 24;
1414         } else {
1415             dayShift = 0;
1416         }
1417         hour -= 24 * dayShift;
1418 
1419         return new DateTimeComponents(new DateComponents(utcComponents.getDate(), dayShift),
1420                                       new TimeComponents(hour, minute, seconds, minutesFromUTC));
1421 
1422     }
1423 
1424     /** {@inheritDoc} */
1425     @Override
1426     public FieldAbsoluteDate<T> getDate() {
1427         return this;
1428     }
1429 
1430     /** Get the field.
1431      * @return field instance.
1432      */
1433     public Field<T> getField() {
1434         return field;
1435     }
1436 
1437     /** Split the instance into date/time components for a time zone.
1438      *
1439      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1440      *
1441      * @param timeZone time zone
1442      * @return date/time components
1443      * @see #getComponents(TimeZone, TimeScale)
1444      */
1445     @DefaultDataContext
1446     public DateTimeComponents getComponents(final TimeZone timeZone) {
1447         return getComponents(timeZone, DataContext.getDefault().getTimeScales().getUTC());
1448     }
1449 
1450     /** Split the instance into date/time components for a time zone.
1451      * @param timeZone time zone
1452      * @param utc            time scale used to compute date and time components.
1453      * @return date/time components
1454      * @since 10.1
1455      */
1456     public DateTimeComponents getComponents(final TimeZone timeZone,
1457                                             final TimeScale utc) {
1458         final FieldAbsoluteDate<T> javaEpoch =
1459                         new FieldAbsoluteDate<>(field, DateComponents.JAVA_EPOCH, utc);
1460         final long milliseconds = FastMath.round((offsetFrom(javaEpoch, utc).getReal()) * 1000);
1461         return getComponents(timeZone.getOffset(milliseconds) / 60000, utc);
1462     }
1463 
1464     /** Compare the instance with another date.
1465      * @param date other date to compare the instance to
1466      * @return a negative integer, zero, or a positive integer as this date
1467      * is before, simultaneous, or after the specified date.
1468      */
1469     public int compareTo(final FieldAbsoluteDate<T> date) {
1470         return Double.compare(durationFrom(date).getReal(), 0.0);
1471     }
1472 
1473 
1474     /** Check if the instance represents the same time as another instance.
1475      * @param date other date
1476      * @return true if the instance and the other date refer to the same instant
1477      */
1478     @SuppressWarnings("unchecked")
1479     public boolean equals(final Object date) {
1480 
1481         if (date == this) {
1482             // first fast check
1483             return true;
1484         }
1485 
1486         if (date instanceof FieldAbsoluteDate) {
1487             return durationFrom((FieldAbsoluteDate<T>) date).getReal() == 0.0;
1488         }
1489 
1490         return false;
1491 
1492     }
1493 
1494     /** Check if the instance represents the same time as another.
1495      * @param other the instant to compare this date to
1496      * @return true if the instance and the argument refer to the same instant
1497      * @see #isCloseTo(FieldTimeStamped, double)
1498      * @since 10.1
1499      */
1500     public boolean isEqualTo(final FieldTimeStamped<T> other) {
1501         return this.equals(other.getDate());
1502     }
1503 
1504     /** Check if the instance time is close to another.
1505      * @param other the instant to compare this date to
1506      * @param tolerance the separation, in seconds, under which the two instants will be considered close to each other
1507      * @return true if the duration between the instance and the argument is strictly below the tolerance
1508      * @see #isEqualTo(FieldTimeStamped)
1509      * @since 10.1
1510      */
1511     public boolean isCloseTo(final FieldTimeStamped<T> other, final double tolerance) {
1512         return FastMath.abs(this.durationFrom(other.getDate()).getReal()) < tolerance;
1513     }
1514 
1515     /** Check if the instance represents a time that is strictly before another.
1516      * @param other the instant to compare this date to
1517      * @return true if the instance is strictly before the argument when ordering chronologically
1518      * @see #isBeforeOrEqualTo(FieldTimeStamped)
1519      * @since 10.1
1520      */
1521     public boolean isBefore(final FieldTimeStamped<T> other) {
1522         return this.compareTo(other.getDate()) < 0;
1523     }
1524 
1525     /** Check if the instance represents a time that is strictly after another.
1526      * @param other the instant to compare this date to
1527      * @return true if the instance is strictly after the argument when ordering chronologically
1528      * @see #isAfterOrEqualTo(FieldTimeStamped)
1529      * @since 10.1
1530      */
1531     public boolean isAfter(final FieldTimeStamped<T> other) {
1532         return this.compareTo(other.getDate()) > 0;
1533     }
1534 
1535     /** Check if the instance represents a time that is before or equal to another.
1536      * @param other the instant to compare this date to
1537      * @return true if the instance is before (or equal to) the argument when ordering chronologically
1538      * @see #isBefore(FieldTimeStamped)
1539      * @since 10.1
1540      */
1541     public boolean isBeforeOrEqualTo(final FieldTimeStamped<T> other) {
1542         return this.isEqualTo(other) || this.isBefore(other);
1543     }
1544 
1545     /** Check if the instance represents a time that is after or equal to another.
1546      * @param other the instant to compare this date to
1547      * @return true if the instance is after (or equal to) the argument when ordering chronologically
1548      * @see #isAfterOrEqualTo(FieldTimeStamped)
1549      * @since 10.1
1550      */
1551     public boolean isAfterOrEqualTo(final FieldTimeStamped<T> other) {
1552         return this.isEqualTo(other) || this.isAfter(other);
1553     }
1554 
1555     /** Check if the instance represents a time that is strictly between two others representing
1556      * the boundaries of a time span. The two boundaries can be provided in any order: in other words,
1557      * whether <code>boundary</code> represents a time that is before or after <code>otherBoundary</code> will
1558      * not change the result of this method.
1559      * @param boundary one end of the time span
1560      * @param otherBoundary the other end of the time span
1561      * @return true if the instance is strictly between the two arguments when ordering chronologically
1562      * @see #isBetweenOrEqualTo(FieldTimeStamped, FieldTimeStamped)
1563      * @since 10.1
1564      */
1565     public boolean isBetween(final FieldTimeStamped<T> boundary, final FieldTimeStamped<T> otherBoundary) {
1566         final FieldTimeStamped<T> beginning;
1567         final FieldTimeStamped<T> end;
1568         if (boundary.getDate().isBefore(otherBoundary)) {
1569             beginning = boundary;
1570             end = otherBoundary;
1571         } else {
1572             beginning = otherBoundary;
1573             end = boundary;
1574         }
1575         return this.isAfter(beginning) && this.isBefore(end);
1576     }
1577 
1578     /** Check if the instance represents a time that is between two others representing
1579      * the boundaries of a time span, or equal to one of them. The two boundaries can be provided in any order:
1580      * in other words, whether <code>boundary</code> represents a time that is before or after
1581      * <code>otherBoundary</code> will not change the result of this method.
1582      * @param boundary one end of the time span
1583      * @param otherBoundary the other end of the time span
1584      * @return true if the instance is between the two arguments (or equal to at least one of them)
1585      * when ordering chronologically
1586      * @see #isBetween(FieldTimeStamped, FieldTimeStamped)
1587      * @since 10.1
1588      */
1589     public boolean isBetweenOrEqualTo(final FieldTimeStamped<T> boundary, final FieldTimeStamped<T> otherBoundary) {
1590         return this.isEqualTo(boundary) || this.isEqualTo(otherBoundary) || this.isBetween(boundary, otherBoundary);
1591     }
1592 
1593     /** Get a hashcode for this date.
1594      * @return hashcode
1595      */
1596     public int hashCode() {
1597         final long l = Double.doubleToLongBits(durationFrom(AbsoluteDate.ARBITRARY_EPOCH).getReal());
1598         return (int) (l ^ (l >>> 32));
1599     }
1600 
1601     /**
1602      * Get a String representation of the instant location with up to 16 digits of
1603      * precision for the seconds value.
1604      *
1605      * <p> Since this method is used in exception messages and error handling every
1606      * effort is made to return some representation of the instant. If UTC is available
1607      * from the default data context then it is used to format the string in UTC. If not
1608      * then TAI is used. Finally if the prior attempts fail this method falls back to
1609      * converting this class's internal representation to a string.
1610      *
1611      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1612      *
1613      * @return a string representation of the instance, in ISO-8601 format if UTC is
1614      * available from the default data context.
1615      * @see AbsoluteDate#toString()
1616      * @see #toString(TimeScale)
1617      * @see DateTimeComponents#toString(int, int)
1618      */
1619     @DefaultDataContext
1620     public String toString() {
1621         return toAbsoluteDate().toString();
1622     }
1623 
1624     /**
1625      * Get a String representation of the instant location in ISO-8601 format without the
1626      * UTC offset and with up to 16 digits of precision for the seconds value.
1627      *
1628      * @param timeScale time scale to use
1629      * @return a string representation of the instance.
1630      * @see DateTimeComponents#toString(int, int)
1631      */
1632     public String toString(final TimeScale timeScale) {
1633         return getComponents(timeScale).toStringWithoutUtcOffset();
1634     }
1635 
1636     /** Get a String representation of the instant location for a local time.
1637      *
1638      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1639      *
1640      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1641      * negative Westward UTC).
1642      * @return string representation of the instance,
1643      * in ISO-8601 format with milliseconds accuracy
1644      * @see #toString(int, TimeScale)
1645      */
1646     @DefaultDataContext
1647     public String toString(final int minutesFromUTC) {
1648         return toString(minutesFromUTC,
1649                         DataContext.getDefault().getTimeScales().getUTC());
1650     }
1651 
1652     /**
1653      * Get a String representation of the instant location for a local time.
1654      *
1655      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
1656      *                       negative Westward UTC).
1657      * @param utc            time scale used to compute date and time components.
1658      * @return string representation of the instance, in ISO-8601 format with milliseconds
1659      * accuracy
1660      * @since 10.1
1661      */
1662     public String toString(final int minutesFromUTC, final TimeScale utc) {
1663         final int minuteDuration = utc.minuteDuration(this);
1664         return getComponents(minutesFromUTC, utc).toString(minuteDuration);
1665     }
1666 
1667     /** Get a String representation of the instant location for a time zone.
1668      *
1669      * <p>This method uses the {@link DataContext#getDefault() default data context}.
1670      *
1671      * @param timeZone time zone
1672      * @return string representation of the instance,
1673      * in ISO-8601 format with milliseconds accuracy
1674      * @see #toString(TimeZone, TimeScale)
1675      */
1676     @DefaultDataContext
1677     public String toString(final TimeZone timeZone) {
1678         return toString(timeZone, DataContext.getDefault().getTimeScales().getUTC());
1679     }
1680 
1681     /**
1682      * Get a String representation of the instant location for a time zone.
1683      *
1684      * @param timeZone time zone
1685      * @param utc      time scale used to compute date and time components.
1686      * @return string representation of the instance, in ISO-8601 format with milliseconds
1687      * accuracy
1688      * @since 10.1
1689      */
1690     public String toString(final TimeZone timeZone, final TimeScale utc) {
1691         final int minuteDuration = utc.minuteDuration(this);
1692         return getComponents(timeZone, utc).toString(minuteDuration);
1693     }
1694 
1695     /**
1696      * Return a string representation of this date-time, rounded to the given precision.
1697      *
1698      * <p>The format used is ISO8601 without the UTC offset.</p>
1699      *
1700      *
1701      * @param timeScale      to use to compute components.
1702      * @param fractionDigits the number of digits to include after the decimal point in
1703      *                       the string representation of the seconds. The date and time
1704      *                       is first rounded as necessary. {@code fractionDigits} must be
1705      *                       greater than or equal to {@code 0}.
1706      * @return string representation of this date, time, and UTC offset
1707      * @see #toString(TimeScale)
1708      * @see DateTimeComponents#toString(int, int)
1709      * @see DateTimeComponents#toStringWithoutUtcOffset(int, int)
1710      * @since 12.2
1711      */
1712     public String toStringWithoutUtcOffset(final TimeScale timeScale,
1713         final int fractionDigits) {
1714         return this.getComponents(timeScale)
1715             .toStringWithoutUtcOffset(timeScale.minuteDuration(this), fractionDigits);
1716     }
1717 
1718     /** Get a time-shifted date.
1719      * <p>
1720      * Calling this method is equivalent to call <code>new FieldAbsoluteDate(this, dt)</code>.
1721      * </p>
1722      * @param dt time shift in seconds
1723      * @return a new date, shifted with respect to instance (which is immutable)
1724      * @see org.orekit.utils.FieldPVCoordinates#shiftedBy(double)
1725      * @see org.orekit.attitudes.FieldAttitude#shiftedBy(double)
1726      * @see org.orekit.orbits.FieldOrbit#shiftedBy(double)
1727      * @see org.orekit.propagation.FieldSpacecraftState#shiftedBy(double)
1728      */
1729     @Override
1730     public FieldAbsoluteDate<T> shiftedBy(final double dt) {
1731         return new FieldAbsoluteDate<>(this, dt);
1732     }
1733 
1734     /** Get a time-shifted date.
1735      * <p>
1736      * Calling this method is equivalent to call <code>new FieldAbsoluteDate(this, dt, timeUnit)</code>.
1737      * </p>
1738      * @param dt time shift in time units
1739      * @param timeUnit {@link TimeUnit} for dt
1740      * @return a new date, shifted with respect to instance (which is immutable)
1741      * @see org.orekit.utils.FieldPVCoordinates#shiftedBy(double)
1742      * @see org.orekit.attitudes.FieldAttitude#shiftedBy(double)
1743      * @see org.orekit.orbits.FieldOrbit#shiftedBy(double)
1744      * @see org.orekit.propagation.FieldSpacecraftState#shiftedBy(double)
1745      * @since 12.1
1746      */
1747     public FieldAbsoluteDate<T> shiftedBy(final long dt, final TimeUnit timeUnit) {
1748         return new FieldAbsoluteDate<>(this, dt, timeUnit);
1749     }
1750 
1751 
1752     /** Transform the FieldAbsoluteDate in an AbsoluteDate.
1753      * @return AbsoluteDate of the FieldObject
1754      * */
1755     public AbsoluteDate toAbsoluteDate() {
1756         return new AbsoluteDate(epoch, offset.getReal());
1757     }
1758 
1759     /** Check if the Field is semantically equal to zero.
1760      *
1761      * <p> Using {@link FieldElement#isZero()}
1762      *
1763      * @return true the Field is semantically equal to zero
1764      * @since 12.0
1765      */
1766     public boolean hasZeroField() {
1767         return (offset instanceof Derivative<?> || offset instanceof Complex) && offset.subtract(offset.getReal()).isZero();
1768     }
1769 }
1770 
1771