time/zone/ZoneRules.java

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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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/*
 * This file is available under and governed by the GNU General Public
 * License version 2 only, as published by the Free Software Foundation.
 * However, the following notice accompanied the original version of this
 * file:
 *
 * Copyright (c) 2009-2012, Stephen Colebourne & Michael Nascimento Santos
 *
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 *  * Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 *
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 *    may be used to endorse or promote products derived from this software
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package java.time.zone;

import java.io.DataInput;
import java.io.DataOutput;
import java.io.IOException;
import java.io.InvalidObjectException;
import java.io.ObjectInputStream;
import java.io.Serializable;
import java.time.Duration;
import java.time.Instant;
import java.time.LocalDateTime;
import java.time.ZoneId;
import java.time.ZoneOffset;
import java.time.Year;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.ConcurrentMap;

/**
 * The rules defining how the zone offset varies for a single time-zone.
 * <p>
 * The rules model all the historic and future transitions for a time-zone.
 * {@link ZoneOffsetTransition} is used for known transitions, typically historic.
 * {@link ZoneOffsetTransitionRule} is used for future transitions that are based
 * on the result of an algorithm.
 * <p>
 * The rules are loaded via {@link ZoneRulesProvider} using a {@link ZoneId}.
 * The same rules may be shared internally between multiple zone IDs.
 * <p>
 * Serializing an instance of {@code ZoneRules} will store the entire set of rules.
 * It does not store the zone ID as it is not part of the state of this object.
 * <p>
 * A rule implementation may or may not store full information about historic
 * and future transitions, and the information stored is only as accurate as
 * that supplied to the implementation by the rules provider.
 * Applications should treat the data provided as representing the best information
 * available to the implementation of this rule.
 *
 * @implSpec
 * This class is immutable and thread-safe.
 *
 * @since 1.8
 */
public final class ZoneRules implements Serializable {

    /**
     * Serialization version.
     */
    private static final long serialVersionUID = 3044319355680032515L;
    /**
     * The last year to have its transitions cached.
     */
    private static final int LAST_CACHED_YEAR = 2100;

    /**
     * The transitions between standard offsets (epoch seconds), sorted.
     */
    private final long[] standardTransitions;
    /**
     * The standard offsets.
     */
    private final ZoneOffset[] standardOffsets;
    /**
     * The transitions between instants (epoch seconds), sorted.
     */
    private final long[] savingsInstantTransitions;
    /**
     * The transitions between local date-times, sorted.
     * This is a paired array, where the first entry is the start of the transition
     * and the second entry is the end of the transition.
     */
    private final LocalDateTime[] savingsLocalTransitions;
    /**
     * The wall offsets.
     */
    private final ZoneOffset[] wallOffsets;
    /**
     * The last rule.
     */
    private final ZoneOffsetTransitionRule[] lastRules;
    /**
     * The map of recent transitions.
     */
    private final transient ConcurrentMap<Integer, ZoneOffsetTransition[]> lastRulesCache =
                new ConcurrentHashMap<Integer, ZoneOffsetTransition[]>();
    /**
     * The zero-length long array.
     */
    private static final long[] EMPTY_LONG_ARRAY = new long[0];
    /**
     * The zero-length lastrules array.
     */
    private static final ZoneOffsetTransitionRule[] EMPTY_LASTRULES =
        new ZoneOffsetTransitionRule[0];
    /**
     * The zero-length ldt array.
     */
    private static final LocalDateTime[] EMPTY_LDT_ARRAY = new LocalDateTime[0];
    /**
     * The number of days in a 400 year cycle.
     */
    private static final int DAYS_PER_CYCLE = 146097;
    /**
     * The number of days from year zero to year 1970.
     * There are five 400 year cycles from year zero to 2000.
     * There are 7 leap years from 1970 to 2000.
     */
    private static final long DAYS_0000_TO_1970 = (DAYS_PER_CYCLE * 5L) - (30L * 365L + 7L);

    /**
     * Obtains an instance of a ZoneRules.
     *
     * @param baseStandardOffset  the standard offset to use before legal rules were set, not null
     * @param baseWallOffset  the wall offset to use before legal rules were set, not null
     * @param standardOffsetTransitionList  the list of changes to the standard offset, not null
     * @param transitionList  the list of transitions, not null
     * @param lastRules  the recurring last rules, size 16 or less, not null
     * @return the zone rules, not null
     */
    public static ZoneRules of(ZoneOffset baseStandardOffset,
                               ZoneOffset baseWallOffset,
                               List<ZoneOffsetTransition> standardOffsetTransitionList,
                               List<ZoneOffsetTransition> transitionList,
                               List<ZoneOffsetTransitionRule> lastRules) {
        Objects.requireNonNull(baseStandardOffset, "baseStandardOffset");
        Objects.requireNonNull(baseWallOffset, "baseWallOffset");
        Objects.requireNonNull(standardOffsetTransitionList, "standardOffsetTransitionList");
        Objects.requireNonNull(transitionList, "transitionList");
        Objects.requireNonNull(lastRules, "lastRules");
        return new ZoneRules(baseStandardOffset, baseWallOffset,
                             standardOffsetTransitionList, transitionList, lastRules);
    }

    /**
     * Obtains an instance of ZoneRules that has fixed zone rules.
     *
     * @param offset  the offset this fixed zone rules is based on, not null
     * @return the zone rules, not null
     * @see #isFixedOffset()
     */
    public static ZoneRules of(ZoneOffset offset) {
        Objects.requireNonNull(offset, "offset");
        return new ZoneRules(offset);
    }

    /**
     * Creates an instance.
     *
     * @param baseStandardOffset  the standard offset to use before legal rules were set, not null
     * @param baseWallOffset  the wall offset to use before legal rules were set, not null
     * @param standardOffsetTransitionList  the list of changes to the standard offset, not null
     * @param transitionList  the list of transitions, not null
     * @param lastRules  the recurring last rules, size 16 or less, not null
     */
    ZoneRules(ZoneOffset baseStandardOffset,
              ZoneOffset baseWallOffset,
              List<ZoneOffsetTransition> standardOffsetTransitionList,
              List<ZoneOffsetTransition> transitionList,
              List<ZoneOffsetTransitionRule> lastRules) {
        super();

        // convert standard transitions

        this.standardTransitions = new long[standardOffsetTransitionList.size()];

        this.standardOffsets = new ZoneOffset[standardOffsetTransitionList.size() + 1];
        this.standardOffsets[0] = baseStandardOffset;
        for (int i = 0; i < standardOffsetTransitionList.size(); i++) {
            this.standardTransitions[i] = standardOffsetTransitionList.get(i).toEpochSecond();
            this.standardOffsets[i + 1] = standardOffsetTransitionList.get(i).getOffsetAfter();
        }

        // convert savings transitions to locals
        List<LocalDateTime> localTransitionList = new ArrayList<>();
        List<ZoneOffset> localTransitionOffsetList = new ArrayList<>();
        localTransitionOffsetList.add(baseWallOffset);
        for (ZoneOffsetTransition trans : transitionList) {
            if (trans.isGap()) {
                localTransitionList.add(trans.getDateTimeBefore());
                localTransitionList.add(trans.getDateTimeAfter());
            } else {
                localTransitionList.add(trans.getDateTimeAfter());
                localTransitionList.add(trans.getDateTimeBefore());
            }
            localTransitionOffsetList.add(trans.getOffsetAfter());
        }
        this.savingsLocalTransitions = localTransitionList.toArray(new LocalDateTime[localTransitionList.size()]);
        this.wallOffsets = localTransitionOffsetList.toArray(new ZoneOffset[localTransitionOffsetList.size()]);

        // convert savings transitions to instants
        this.savingsInstantTransitions = new long[transitionList.size()];
        for (int i = 0; i < transitionList.size(); i++) {
            this.savingsInstantTransitions[i] = transitionList.get(i).toEpochSecond();
        }

        // last rules
        if (lastRules.size() > 16) {
            throw new IllegalArgumentException("Too many transition rules");
        }
        this.lastRules = lastRules.toArray(new ZoneOffsetTransitionRule[lastRules.size()]);
    }

    /**
     * Constructor.
     *
     * @param standardTransitions  the standard transitions, not null
     * @param standardOffsets  the standard offsets, not null
     * @param savingsInstantTransitions  the standard transitions, not null
     * @param wallOffsets  the wall offsets, not null
     * @param lastRules  the recurring last rules, size 15 or less, not null
     */
    private ZoneRules(long[] standardTransitions,
                      ZoneOffset[] standardOffsets,
                      long[] savingsInstantTransitions,
                      ZoneOffset[] wallOffsets,
                      ZoneOffsetTransitionRule[] lastRules) {
        super();

        this.standardTransitions = standardTransitions;
        this.standardOffsets = standardOffsets;
        this.savingsInstantTransitions = savingsInstantTransitions;
        this.wallOffsets = wallOffsets;
        this.lastRules = lastRules;

        if (savingsInstantTransitions.length == 0) {
            this.savingsLocalTransitions = EMPTY_LDT_ARRAY;
        } else {
            // convert savings transitions to locals
            List<LocalDateTime> localTransitionList = new ArrayList<>();
            for (int i = 0; i < savingsInstantTransitions.length; i++) {
                ZoneOffset before = wallOffsets[i];
                ZoneOffset after = wallOffsets[i + 1];
                ZoneOffsetTransition trans = new ZoneOffsetTransition(savingsInstantTransitions[i], before, after);
                if (trans.isGap()) {
                    localTransitionList.add(trans.getDateTimeBefore());
                    localTransitionList.add(trans.getDateTimeAfter());
                } else {
                    localTransitionList.add(trans.getDateTimeAfter());
                    localTransitionList.add(trans.getDateTimeBefore());
               }
            }
            this.savingsLocalTransitions = localTransitionList.toArray(new LocalDateTime[localTransitionList.size()]);
        }
    }

    /**
     * Creates an instance of ZoneRules that has fixed zone rules.
     *
     * @param offset  the offset this fixed zone rules is based on, not null
     * @see #isFixedOffset()
     */
    private ZoneRules(ZoneOffset offset) {
        this.standardOffsets = new ZoneOffset[1];
        this.standardOffsets[0] = offset;
        this.standardTransitions = EMPTY_LONG_ARRAY;
        this.savingsInstantTransitions = EMPTY_LONG_ARRAY;
        this.savingsLocalTransitions = EMPTY_LDT_ARRAY;
        this.wallOffsets = standardOffsets;
        this.lastRules = EMPTY_LASTRULES;
    }

    /**
     * Defend against malicious streams.
     *
     * @param s the stream to read
     * @throws InvalidObjectException always
     */
    private void readObject(ObjectInputStream s) throws InvalidObjectException {
        throw new InvalidObjectException("Deserialization via serialization delegate");
    }

    /**
     * Writes the object using a
     * <a href="{@docRoot}/serialized-form.html#java.time.zone.Ser">dedicated serialized form</a>.
     * @serialData
     * <pre style="font-size:1.0em">{@code
     *
     *   out.writeByte(1);  // identifies a ZoneRules
     *   out.writeInt(standardTransitions.length);
     *   for (long trans : standardTransitions) {
     *       Ser.writeEpochSec(trans, out);
     *   }
     *   for (ZoneOffset offset : standardOffsets) {
     *       Ser.writeOffset(offset, out);
     *   }
     *   out.writeInt(savingsInstantTransitions.length);
     *   for (long trans : savingsInstantTransitions) {
     *       Ser.writeEpochSec(trans, out);
     *   }
     *   for (ZoneOffset offset : wallOffsets) {
     *       Ser.writeOffset(offset, out);
     *   }
     *   out.writeByte(lastRules.length);
     *   for (ZoneOffsetTransitionRule rule : lastRules) {
     *       rule.writeExternal(out);
     *   }
     * }
     * </pre>
     * <p>
     * Epoch second values used for offsets are encoded in a variable
     * length form to make the common cases put fewer bytes in the stream.
     * <pre style="font-size:1.0em">{@code
     *
     *  static void writeEpochSec(long epochSec, DataOutput out) throws IOException {
     *     if (epochSec >= -4575744000L && epochSec < 10413792000L && epochSec % 900 == 0) {  // quarter hours between 1825 and 2300
     *         int store = (int) ((epochSec + 4575744000L) / 900);
     *         out.writeByte((store >>> 16) & 255);
     *         out.writeByte((store >>> 8) & 255);
     *         out.writeByte(store & 255);
     *      } else {
     *          out.writeByte(255);
     *          out.writeLong(epochSec);
     *      }
     *  }
     * }
     * </pre>
     * <p>
     * ZoneOffset values are encoded in a variable length form so the
     * common cases put fewer bytes in the stream.
     * <pre style="font-size:1.0em">{@code
     *
     *  static void writeOffset(ZoneOffset offset, DataOutput out) throws IOException {
     *     final int offsetSecs = offset.getTotalSeconds();
     *     int offsetByte = offsetSecs % 900 == 0 ? offsetSecs / 900 : 127;  // compress to -72 to +72
     *     out.writeByte(offsetByte);
     *     if (offsetByte == 127) {
     *         out.writeInt(offsetSecs);
     *     }
     * }
     *}
     * </pre>
     * @return the replacing object, not null
     */
    private Object writeReplace() {
        return new Ser(Ser.ZRULES, this);
    }

    /**
     * Writes the state to the stream.
     *
     * @param out  the output stream, not null
     * @throws IOException if an error occurs
     */
    void writeExternal(DataOutput out) throws IOException {
        out.writeInt(standardTransitions.length);
        for (long trans : standardTransitions) {
            Ser.writeEpochSec(trans, out);
        }
        for (ZoneOffset offset : standardOffsets) {
            Ser.writeOffset(offset, out);
        }
        out.writeInt(savingsInstantTransitions.length);
        for (long trans : savingsInstantTransitions) {
            Ser.writeEpochSec(trans, out);
        }
        for (ZoneOffset offset : wallOffsets) {
            Ser.writeOffset(offset, out);
        }
        out.writeByte(lastRules.length);
        for (ZoneOffsetTransitionRule rule : lastRules) {
            rule.writeExternal(out);
        }
    }

    /**
     * Reads the state from the stream. The 1,024 limit to the lengths
     * of stdTrans and savSize is intended to be the size well enough
     * to accommodate the max number of transitions in current tzdb data
     * (203 for Asia/Tehran).
     *
     * @param in  the input stream, not null
     * @return the created object, not null
     * @throws IOException if an error occurs
     */
    static ZoneRules readExternal(DataInput in) throws IOException, ClassNotFoundException {
        int stdSize = in.readInt();
        if (stdSize > 1024) {
            throw new InvalidObjectException("Too many transitions");
        }
        long[] stdTrans = (stdSize == 0) ? EMPTY_LONG_ARRAY
                                         : new long[stdSize];
        for (int i = 0; i < stdSize; i++) {
            stdTrans[i] = Ser.readEpochSec(in);
        }
        ZoneOffset[] stdOffsets = new ZoneOffset[stdSize + 1];
        for (int i = 0; i < stdOffsets.length; i++) {
            stdOffsets[i] = Ser.readOffset(in);
        }
        int savSize = in.readInt();
        if (savSize > 1024) {
            throw new InvalidObjectException("Too many saving offsets");
        }
        long[] savTrans = (savSize == 0) ? EMPTY_LONG_ARRAY
                                         : new long[savSize];
        for (int i = 0; i < savSize; i++) {
            savTrans[i] = Ser.readEpochSec(in);
        }
        ZoneOffset[] savOffsets = new ZoneOffset[savSize + 1];
        for (int i = 0; i < savOffsets.length; i++) {
            savOffsets[i] = Ser.readOffset(in);
        }
        int ruleSize = in.readByte();
        if (ruleSize > 16) {
            throw new InvalidObjectException("Too many transition rules");
        }
        ZoneOffsetTransitionRule[] rules = (ruleSize == 0) ?
            EMPTY_LASTRULES : new ZoneOffsetTransitionRule[ruleSize];
        for (int i = 0; i < ruleSize; i++) {
            rules[i] = ZoneOffsetTransitionRule.readExternal(in);
        }
        return new ZoneRules(stdTrans, stdOffsets, savTrans, savOffsets, rules);
    }

    /**
     * Checks of the zone rules are fixed, such that the offset never varies.
     *
     * @return true if the time-zone is fixed and the offset never changes
     */
    public boolean isFixedOffset() {
        return standardOffsets[0].equals(wallOffsets[0]) &&
                standardTransitions.length == 0 &&
                savingsInstantTransitions.length == 0 &&
                lastRules.length == 0;
    }

    /**
     * Gets the offset applicable at the specified instant in these rules.
     * <p>
     * The mapping from an instant to an offset is simple, there is only
     * one valid offset for each instant.
     * This method returns that offset.
     *
     * @param instant  the instant to find the offset for, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the offset, not null
     */
    public ZoneOffset getOffset(Instant instant) {
        if (savingsInstantTransitions.length == 0) {
            return wallOffsets[0];
        }
        long epochSec = instant.getEpochSecond();
        // check if using last rules
        if (lastRules.length > 0 &&
                epochSec > savingsInstantTransitions[savingsInstantTransitions.length - 1]) {
            int year = findYear(epochSec, wallOffsets[wallOffsets.length - 1]);
            ZoneOffsetTransition[] transArray = findTransitionArray(year);
            ZoneOffsetTransition trans = null;
            for (int i = 0; i < transArray.length; i++) {
                trans = transArray[i];
                if (epochSec < trans.toEpochSecond()) {
                    return trans.getOffsetBefore();
                }
            }
            return trans.getOffsetAfter();
        }

        // using historic rules
        int index  = Arrays.binarySearch(savingsInstantTransitions, epochSec);
        if (index < 0) {
            // switch negative insert position to start of matched range
            index = -index - 2;
        }
        return wallOffsets[index + 1];
    }

    /**
     * Gets a suitable offset for the specified local date-time in these rules.
     * <p>
     * The mapping from a local date-time to an offset is not straightforward.
     * There are three cases:
     * <ul>
     * <li>Normal, with one valid offset. For the vast majority of the year, the normal
     *  case applies, where there is a single valid offset for the local date-time.</li>
     * <li>Gap, with zero valid offsets. This is when clocks jump forward typically
     *  due to the spring daylight savings change from "winter" to "summer".
     *  In a gap there are local date-time values with no valid offset.</li>
     * <li>Overlap, with two valid offsets. This is when clocks are set back typically
     *  due to the autumn daylight savings change from "summer" to "winter".
     *  In an overlap there are local date-time values with two valid offsets.</li>
     * </ul>
     * Thus, for any given local date-time there can be zero, one or two valid offsets.
     * This method returns the single offset in the Normal case, and in the Gap or Overlap
     * case it returns the offset before the transition.
     * <p>
     * Since, in the case of Gap and Overlap, the offset returned is a "best" value, rather
     * than the "correct" value, it should be treated with care. Applications that care
     * about the correct offset should use a combination of this method,
     * {@link #getValidOffsets(LocalDateTime)} and {@link #getTransition(LocalDateTime)}.
     *
     * @param localDateTime  the local date-time to query, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the best available offset for the local date-time, not null
     */
    public ZoneOffset getOffset(LocalDateTime localDateTime) {
        Object info = getOffsetInfo(localDateTime);
        if (info instanceof ZoneOffsetTransition) {
            return ((ZoneOffsetTransition) info).getOffsetBefore();
        }
        return (ZoneOffset) info;
    }

    /**
     * Gets the offset applicable at the specified local date-time in these rules.
     * <p>
     * The mapping from a local date-time to an offset is not straightforward.
     * There are three cases:
     * <ul>
     * <li>Normal, with one valid offset. For the vast majority of the year, the normal
     *  case applies, where there is a single valid offset for the local date-time.</li>
     * <li>Gap, with zero valid offsets. This is when clocks jump forward typically
     *  due to the spring daylight savings change from "winter" to "summer".
     *  In a gap there are local date-time values with no valid offset.</li>
     * <li>Overlap, with two valid offsets. This is when clocks are set back typically
     *  due to the autumn daylight savings change from "summer" to "winter".
     *  In an overlap there are local date-time values with two valid offsets.</li>
     * </ul>
     * Thus, for any given local date-time there can be zero, one or two valid offsets.
     * This method returns that list of valid offsets, which is a list of size 0, 1 or 2.
     * In the case where there are two offsets, the earlier offset is returned at index 0
     * and the later offset at index 1.
     * <p>
     * There are various ways to handle the conversion from a {@code LocalDateTime}.
     * One technique, using this method, would be:
     * <pre>
     *  List&lt;ZoneOffset&gt; validOffsets = rules.getValidOffsets(localDT);
     *  if (validOffsets.size() == 1) {
     *    // Normal case: only one valid offset
     *    zoneOffset = validOffsets.get(0);
     *  } else {
     *    // Gap or Overlap: determine what to do from transition (which will be non-null)
     *    ZoneOffsetTransition trans = rules.getTransition(localDT);
     *  }
     * </pre>
     * <p>
     * In theory, it is possible for there to be more than two valid offsets.
     * This would happen if clocks to be put back more than once in quick succession.
     * This has never happened in the history of time-zones and thus has no special handling.
     * However, if it were to happen, then the list would return more than 2 entries.
     *
     * @param localDateTime  the local date-time to query for valid offsets, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the list of valid offsets, may be immutable, not null
     */
    public List<ZoneOffset> getValidOffsets(LocalDateTime localDateTime) {
        // should probably be optimized
        Object info = getOffsetInfo(localDateTime);
        if (info instanceof ZoneOffsetTransition) {
            return ((ZoneOffsetTransition) info).getValidOffsets();
        }
        return Collections.singletonList((ZoneOffset) info);
    }

    /**
     * Gets the offset transition applicable at the specified local date-time in these rules.
     * <p>
     * The mapping from a local date-time to an offset is not straightforward.
     * There are three cases:
     * <ul>
     * <li>Normal, with one valid offset. For the vast majority of the year, the normal
     *  case applies, where there is a single valid offset for the local date-time.</li>
     * <li>Gap, with zero valid offsets. This is when clocks jump forward typically
     *  due to the spring daylight savings change from "winter" to "summer".
     *  In a gap there are local date-time values with no valid offset.</li>
     * <li>Overlap, with two valid offsets. This is when clocks are set back typically
     *  due to the autumn daylight savings change from "summer" to "winter".
     *  In an overlap there are local date-time values with two valid offsets.</li>
     * </ul>
     * A transition is used to model the cases of a Gap or Overlap.
     * The Normal case will return null.
     * <p>
     * There are various ways to handle the conversion from a {@code LocalDateTime}.
     * One technique, using this method, would be:
     * <pre>
     *  ZoneOffsetTransition trans = rules.getTransition(localDT);
     *  if (trans != null) {
     *    // Gap or Overlap: determine what to do from transition
     *  } else {
     *    // Normal case: only one valid offset
     *    zoneOffset = rule.getOffset(localDT);
     *  }
     * </pre>
     *
     * @param localDateTime  the local date-time to query for offset transition, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the offset transition, null if the local date-time is not in transition
     */
    public ZoneOffsetTransition getTransition(LocalDateTime localDateTime) {
        Object info = getOffsetInfo(localDateTime);
        return (info instanceof ZoneOffsetTransition ? (ZoneOffsetTransition) info : null);
    }

    private Object getOffsetInfo(LocalDateTime dt) {
        if (savingsLocalTransitions.length == 0) {
            return wallOffsets[0];
        }
        // check if using last rules
        if (lastRules.length > 0 &&
                dt.isAfter(savingsLocalTransitions[savingsLocalTransitions.length - 1])) {
            ZoneOffsetTransition[] transArray = findTransitionArray(dt.getYear());
            Object info = null;
            for (ZoneOffsetTransition trans : transArray) {
                info = findOffsetInfo(dt, trans);
                if (info instanceof ZoneOffsetTransition || info.equals(trans.getOffsetBefore())) {
                    return info;
                }
            }
            return info;
        }

        // using historic rules
        int index  = Arrays.binarySearch(savingsLocalTransitions, dt);
        if (index == -1) {
            // before first transition
            return wallOffsets[0];
        }
        if (index < 0) {
            // switch negative insert position to start of matched range
            index = -index - 2;
        } else if (index < savingsLocalTransitions.length - 1 &&
                savingsLocalTransitions[index].equals(savingsLocalTransitions[index + 1])) {
            // handle overlap immediately following gap
            index++;
        }
        if ((index & 1) == 0) {
            // gap or overlap
            LocalDateTime dtBefore = savingsLocalTransitions[index];
            LocalDateTime dtAfter = savingsLocalTransitions[index + 1];
            ZoneOffset offsetBefore = wallOffsets[index / 2];
            ZoneOffset offsetAfter = wallOffsets[index / 2 + 1];
            if (offsetAfter.getTotalSeconds() > offsetBefore.getTotalSeconds()) {
                // gap
                return new ZoneOffsetTransition(dtBefore, offsetBefore, offsetAfter);
            } else {
                // overlap
                return new ZoneOffsetTransition(dtAfter, offsetBefore, offsetAfter);
            }
        } else {
            // normal (neither gap or overlap)
            return wallOffsets[index / 2 + 1];
        }
    }

    /**
     * Finds the offset info for a local date-time and transition.
     *
     * @param dt  the date-time, not null
     * @param trans  the transition, not null
     * @return the offset info, not null
     */
    private Object findOffsetInfo(LocalDateTime dt, ZoneOffsetTransition trans) {
        LocalDateTime localTransition = trans.getDateTimeBefore();
        if (trans.isGap()) {
            if (dt.isBefore(localTransition)) {
                return trans.getOffsetBefore();
            }
            if (dt.isBefore(trans.getDateTimeAfter())) {
                return trans;
            } else {
                return trans.getOffsetAfter();
            }
        } else {
            if (dt.isBefore(localTransition) == false) {
                return trans.getOffsetAfter();
            }
            if (dt.isBefore(trans.getDateTimeAfter())) {
                return trans.getOffsetBefore();
            } else {
                return trans;
            }
        }
    }

    /**
     * Finds the appropriate transition array for the given year.
     *
     * @param year  the year, not null
     * @return the transition array, not null
     */
    private ZoneOffsetTransition[] findTransitionArray(int year) {
        Integer yearObj = year;  // should use Year class, but this saves a class load
        ZoneOffsetTransition[] transArray = lastRulesCache.get(yearObj);
        if (transArray != null) {
            return transArray;
        }
        ZoneOffsetTransitionRule[] ruleArray = lastRules;
        transArray  = new ZoneOffsetTransition[ruleArray.length];
        for (int i = 0; i < ruleArray.length; i++) {
            transArray[i] = ruleArray[i].createTransition(year);
        }
        if (year < LAST_CACHED_YEAR) {
            lastRulesCache.putIfAbsent(yearObj, transArray);
        }
        return transArray;
    }

    /**
     * Gets the standard offset for the specified instant in this zone.
     * <p>
     * This provides access to historic information on how the standard offset
     * has changed over time.
     * The standard offset is the offset before any daylight saving time is applied.
     * This is typically the offset applicable during winter.
     *
     * @param instant  the instant to find the offset information for, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the standard offset, not null
     */
    public ZoneOffset getStandardOffset(Instant instant) {
        if (standardTransitions.length == 0) {
            return standardOffsets[0];
        }
        long epochSec = instant.getEpochSecond();
        int index  = Arrays.binarySearch(standardTransitions, epochSec);
        if (index < 0) {
            // switch negative insert position to start of matched range
            index = -index - 2;
        }
        return standardOffsets[index + 1];
    }

    /**
     * Gets the amount of daylight savings in use for the specified instant in this zone.
     * <p>
     * This provides access to historic information on how the amount of daylight
     * savings has changed over time.
     * This is the difference between the standard offset and the actual offset.
     * Typically the amount is zero during winter and one hour during summer.
     * Time-zones are second-based, so the nanosecond part of the duration will be zero.
     * <p>
     * This default implementation calculates the duration from the
     * {@link #getOffset(java.time.Instant) actual} and
     * {@link #getStandardOffset(java.time.Instant) standard} offsets.
     *
     * @param instant  the instant to find the daylight savings for, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the difference between the standard and actual offset, not null
     */
    public Duration getDaylightSavings(Instant instant) {
        if (isFixedOffset()) {
            return Duration.ZERO;
        }
        ZoneOffset standardOffset = getStandardOffset(instant);
        ZoneOffset actualOffset = getOffset(instant);
        return Duration.ofSeconds(actualOffset.getTotalSeconds() - standardOffset.getTotalSeconds());
    }

    /**
     * Checks if the specified instant is in daylight savings.
     * <p>
     * This checks if the standard offset and the actual offset are the same
     * for the specified instant.
     * If they are not, it is assumed that daylight savings is in operation.
     * <p>
     * This default implementation compares the {@link #getOffset(java.time.Instant) actual}
     * and {@link #getStandardOffset(java.time.Instant) standard} offsets.
     *
     * @param instant  the instant to find the offset information for, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the standard offset, not null
     */
    public boolean isDaylightSavings(Instant instant) {
        return (getStandardOffset(instant).equals(getOffset(instant)) == false);
    }

    /**
     * Checks if the offset date-time is valid for these rules.
     * <p>
     * To be valid, the local date-time must not be in a gap and the offset
     * must match one of the valid offsets.
     * <p>
     * This default implementation checks if {@link #getValidOffsets(java.time.LocalDateTime)}
     * contains the specified offset.
     *
     * @param localDateTime  the date-time to check, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @param offset  the offset to check, null returns false
     * @return true if the offset date-time is valid for these rules
     */
    public boolean isValidOffset(LocalDateTime localDateTime, ZoneOffset offset) {
        return getValidOffsets(localDateTime).contains(offset);
    }

    /**
     * Gets the next transition after the specified instant.
     * <p>
     * This returns details of the next transition after the specified instant.
     * For example, if the instant represents a point where "Summer" daylight savings time
     * applies, then the method will return the transition to the next "Winter" time.
     *
     * @param instant  the instant to get the next transition after, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the next transition after the specified instant, null if this is after the last transition
     */
    public ZoneOffsetTransition nextTransition(Instant instant) {
        if (savingsInstantTransitions.length == 0) {
            return null;
        }
        long epochSec = instant.getEpochSecond();
        // check if using last rules
        if (epochSec >= savingsInstantTransitions[savingsInstantTransitions.length - 1]) {
            if (lastRules.length == 0) {
                return null;
            }
            // search year the instant is in
            int year = findYear(epochSec, wallOffsets[wallOffsets.length - 1]);
            ZoneOffsetTransition[] transArray = findTransitionArray(year);
            for (ZoneOffsetTransition trans : transArray) {
                if (epochSec < trans.toEpochSecond()) {
                    return trans;
                }
            }
            // use first from following year
            if (year < Year.MAX_VALUE) {
                transArray = findTransitionArray(year + 1);
                return transArray[0];
            }
            return null;
        }

        // using historic rules
        int index  = Arrays.binarySearch(savingsInstantTransitions, epochSec);
        if (index < 0) {
            index = -index - 1;  // switched value is the next transition
        } else {
            index += 1;  // exact match, so need to add one to get the next
        }
        return new ZoneOffsetTransition(savingsInstantTransitions[index], wallOffsets[index], wallOffsets[index + 1]);
    }

    /**
     * Gets the previous transition before the specified instant.
     * <p>
     * This returns details of the previous transition before the specified instant.
     * For example, if the instant represents a point where "summer" daylight saving time
     * applies, then the method will return the transition from the previous "winter" time.
     *
     * @param instant  the instant to get the previous transition after, not null, but null
     *  may be ignored if the rules have a single offset for all instants
     * @return the previous transition before the specified instant, null if this is before the first transition
     */
    public ZoneOffsetTransition previousTransition(Instant instant) {
        if (savingsInstantTransitions.length == 0) {
            return null;
        }
        long epochSec = instant.getEpochSecond();
        if (instant.getNano() > 0 && epochSec < Long.MAX_VALUE) {
            epochSec += 1;  // allow rest of method to only use seconds
        }

        // check if using last rules
        long lastHistoric = savingsInstantTransitions[savingsInstantTransitions.length - 1];
        if (lastRules.length > 0 && epochSec > lastHistoric) {
            // search year the instant is in
            ZoneOffset lastHistoricOffset = wallOffsets[wallOffsets.length - 1];
            int year = findYear(epochSec, lastHistoricOffset);
            ZoneOffsetTransition[] transArray = findTransitionArray(year);
            for (int i = transArray.length - 1; i >= 0; i--) {
                if (epochSec > transArray[i].toEpochSecond()) {
                    return transArray[i];
                }
            }
            // use last from preceding year
            int lastHistoricYear = findYear(lastHistoric, lastHistoricOffset);
            if (--year > lastHistoricYear) {
                transArray = findTransitionArray(year);
                return transArray[transArray.length - 1];
            }
            // drop through
        }

        // using historic rules
        int index  = Arrays.binarySearch(savingsInstantTransitions, epochSec);
        if (index < 0) {
            index = -index - 1;
        }
        if (index <= 0) {
            return null;
        }
        return new ZoneOffsetTransition(savingsInstantTransitions[index - 1], wallOffsets[index - 1], wallOffsets[index]);
    }

    private int findYear(long epochSecond, ZoneOffset offset) {
        long localSecond = epochSecond + offset.getTotalSeconds();
        long zeroDay = Math.floorDiv(localSecond, 86400) + DAYS_0000_TO_1970;

        // find the march-based year
        zeroDay -= 60;  // adjust to 0000-03-01 so leap day is at end of four year cycle
        long adjust = 0;
        if (zeroDay < 0) {
            // adjust negative years to positive for calculation
            long adjustCycles = (zeroDay + 1) / DAYS_PER_CYCLE - 1;
            adjust = adjustCycles * 400;
            zeroDay += -adjustCycles * DAYS_PER_CYCLE;
        }
        long yearEst = (400 * zeroDay + 591) / DAYS_PER_CYCLE;
        long doyEst = zeroDay - (365 * yearEst + yearEst / 4 - yearEst / 100 + yearEst / 400);
        if (doyEst < 0) {
            // fix estimate
            yearEst--;
            doyEst = zeroDay - (365 * yearEst + yearEst / 4 - yearEst / 100 + yearEst / 400);
        }
        yearEst += adjust;  // reset any negative year
        int marchDoy0 = (int) doyEst;

        // convert march-based values back to january-based
        int marchMonth0 = (marchDoy0 * 5 + 2) / 153;
        yearEst += marchMonth0 / 10;

        // Cap to the max value
        return (int)Math.min(yearEst, Year.MAX_VALUE);
    }

    /**
     * Gets the complete list of fully defined transitions.
     * <p>
     * The complete set of transitions for this rules instance is defined by this method
     * and {@link #getTransitionRules()}. This method returns those transitions that have
     * been fully defined. These are typically historical, but may be in the future.
     * <p>
     * The list will be empty for fixed offset rules and for any time-zone where there has
     * only ever been a single offset. The list will also be empty if the transition rules are unknown.
     *
     * @return an immutable list of fully defined transitions, not null
     */
    public List<ZoneOffsetTransition> getTransitions() {
        List<ZoneOffsetTransition> list = new ArrayList<>();
        for (int i = 0; i < savingsInstantTransitions.length; i++) {
            list.add(new ZoneOffsetTransition(savingsInstantTransitions[i], wallOffsets[i], wallOffsets[i + 1]));
        }
        return Collections.unmodifiableList(list);
    }

    /**
     * Gets the list of transition rules for years beyond those defined in the transition list.
     * <p>
     * The complete set of transitions for this rules instance is defined by this method
     * and {@link #getTransitions()}. This method returns instances of {@link ZoneOffsetTransitionRule}
     * that define an algorithm for when transitions will occur.
     * <p>
     * For any given {@code ZoneRules}, this list contains the transition rules for years
     * beyond those years that have been fully defined. These rules typically refer to future
     * daylight saving time rule changes.
     * <p>
     * If the zone defines daylight savings into the future, then the list will normally
     * be of size two and hold information about entering and exiting daylight savings.
     * If the zone does not have daylight savings, or information about future changes
     * is uncertain, then the list will be empty.
     * <p>
     * The list will be empty for fixed offset rules and for any time-zone where there is no
     * daylight saving time. The list will also be empty if the transition rules are unknown.
     *
     * @return an immutable list of transition rules, not null
     */
    public List<ZoneOffsetTransitionRule> getTransitionRules() {
        return List.of(lastRules);
    }

    /**
     * Checks if this set of rules equals another.
     * <p>
     * Two rule sets are equal if they will always result in the same output
     * for any given input instant or local date-time.
     * Rules from two different groups may return false even if they are in fact the same.
     * <p>
     * This definition should result in implementations comparing their entire state.
     *
     * @param otherRules  the other rules, null returns false
     * @return true if this rules is the same as that specified
     */
    @Override
    public boolean equals(Object otherRules) {
        if (this == otherRules) {
           return true;
        }
        if (otherRules instanceof ZoneRules) {
            ZoneRules other = (ZoneRules) otherRules;
            return Arrays.equals(standardTransitions, other.standardTransitions) &&
                    Arrays.equals(standardOffsets, other.standardOffsets) &&
                    Arrays.equals(savingsInstantTransitions, other.savingsInstantTransitions) &&
                    Arrays.equals(wallOffsets, other.wallOffsets) &&
                    Arrays.equals(lastRules, other.lastRules);
        }
        return false;
    }

    /**
     * Returns a suitable hash code given the definition of {@code #equals}.
     *
     * @return the hash code
     */
    @Override
    public int hashCode() {
        return Arrays.hashCode(standardTransitions) ^
                Arrays.hashCode(standardOffsets) ^
                Arrays.hashCode(savingsInstantTransitions) ^
                Arrays.hashCode(wallOffsets) ^
                Arrays.hashCode(lastRules);
    }

    /**
     * Returns a string describing this object.
     *
     * @return a string for debugging, not null
     */
    @Override
    public String toString() {
        return "ZoneRules[currentStandardOffset=" + standardOffsets[standardOffsets.length - 1] + "]";
    }

}