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/*
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 * Copyright (c) 2008-2012, 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.
 *
 * * Redistributions in binary form must reproduce the above copyright notice,
 * this list of conditions and the following disclaimer in the documentation
 * and/or other materials provided with the distribution.
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 * * Neither the name of JSR-310 nor the names of its contributors
 * may be used to endorse or promote products derived from this software
 * without specific prior written permission.
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 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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 */
package java.time;

import static java.time.temporal.ChronoUnit.DAYS;
import static java.time.temporal.ChronoUnit.MONTHS;
import static java.time.temporal.ChronoUnit.YEARS;

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.chrono.ChronoLocalDate;
import java.time.chrono.ChronoPeriod;
import java.time.chrono.Chronology;
import java.time.chrono.IsoChronology;
import java.time.format.DateTimeParseException;
import java.time.temporal.ChronoUnit;
import java.time.temporal.Temporal;
import java.time.temporal.TemporalAccessor;
import java.time.temporal.TemporalAmount;
import java.time.temporal.TemporalQueries;
import java.time.temporal.TemporalUnit;
import java.time.temporal.UnsupportedTemporalTypeException;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

/**
 * A date-based amount of time in the ISO-8601 calendar system,
 * such as '2 years, 3 months and 4 days'.
 * <p>
 * This class models a quantity or amount of time in terms of years, months and days.
 * See {@link Duration} for the time-based equivalent to this class.
 * <p>
 * Durations and periods differ in their treatment of daylight savings time
 * when added to {@link ZonedDateTime}. A {@code Duration} will add an exact
 * number of seconds, thus a duration of one day is always exactly 24 hours.
 * By contrast, a {@code Period} will add a conceptual day, trying to maintain
 * the local time.
 * <p>
 * For example, consider adding a period of one day and a duration of one day to
 * 18:00 on the evening before a daylight savings gap. The {@code Period} will add
 * the conceptual day and result in a {@code ZonedDateTime} at 18:00 the following day.
 * By contrast, the {@code Duration} will add exactly 24 hours, resulting in a
 * {@code ZonedDateTime} at 19:00 the following day (assuming a one hour DST gap).
 * <p>
 * The supported units of a period are {@link ChronoUnit#YEARS YEARS},
 * {@link ChronoUnit#MONTHS MONTHS} and {@link ChronoUnit#DAYS DAYS}.
 * All three fields are always present, but may be set to zero.
 * <p>
 * The ISO-8601 calendar system is the modern civil calendar system used today
 * in most of the world. It is equivalent to the proleptic Gregorian calendar
 * system, in which today's rules for leap years are applied for all time.
 * <p>
 * The period is modeled as a directed amount of time, meaning that individual parts of the
 * period may be negative.
 *
 * <p>
 * This is a <a href="{@docRoot}/java/lang/doc-files/ValueBased.html">value-based</a>
 * class; use of identity-sensitive operations (including reference equality
 * ({@code ==}), identity hash code, or synchronization) on instances of
 * {@code Period} may have unpredictable results and should be avoided.
 * The {@code equals} method should be used for comparisons.
 *
 * @implSpec
 * This class is immutable and thread-safe.
 *
 * @since 1.8
 */
public final class Period
 implements ChronoPeriod, Serializable {

 /**
 * A constant for a period of zero.
 */
 public static final Period ZERO = new Period(0, 0, 0);
 /**
 * Serialization version.
 */
 private static final long serialVersionUID = -3587258372562876L;
 /**
 * The pattern for parsing.
 */
 private static final Pattern PATTERN =
 Pattern.compile("([-+]?)P(?:([-+]?[0-9]+)Y)?(?:([-+]?[0-9]+)M)?(?:([-+]?[0-9]+)W)?(?:([-+]?[0-9]+)D)?", Pattern.CASE_INSENSITIVE);

 /**
 * The set of supported units.
 */
 private static final List<TemporalUnit> SUPPORTED_UNITS =
 Collections.unmodifiableList(Arrays.<TemporalUnit>asList(YEARS, MONTHS, DAYS));

 /**
 * The number of years.
 */
 private final int years;
 /**
 * The number of months.
 */
 private final int months;
 /**
 * The number of days.
 */
 private final int days;

 //-----------------------------------------------------------------------
 /**
 * Obtains a {@code Period} representing a number of years.
 * <p>
 * The resulting period will have the specified years.
 * The months and days units will be zero.
 *
 * @param years the number of years, positive or negative
 * @return the period of years, not null
 */
 public static Period ofYears(int years) {
 return create(years, 0, 0);
 }

 /**
 * Obtains a {@code Period} representing a number of months.
 * <p>
 * The resulting period will have the specified months.
 * The years and days units will be zero.
 *
 * @param months the number of months, positive or negative
 * @return the period of months, not null
 */
 public static Period ofMonths(int months) {
 return create(0, months, 0);
 }

 /**
 * Obtains a {@code Period} representing a number of weeks.
 * <p>
 * The resulting period will be day-based, with the amount of days
 * equal to the number of weeks multiplied by 7.
 * The years and months units will be zero.
 *
 * @param weeks the number of weeks, positive or negative
 * @return the period, with the input weeks converted to days, not null
 */
 public static Period ofWeeks(int weeks) {
 return create(0, 0, Math.multiplyExact(weeks, 7));
 }

 /**
 * Obtains a {@code Period} representing a number of days.
 * <p>
 * The resulting period will have the specified days.
 * The years and months units will be zero.
 *
 * @param days the number of days, positive or negative
 * @return the period of days, not null
 */
 public static Period ofDays(int days) {
 return create(0, 0, days);
 }

 //-----------------------------------------------------------------------
 /**
 * Obtains a {@code Period} representing a number of years, months and days.
 * <p>
 * This creates an instance based on years, months and days.
 *
 * @param years the amount of years, may be negative
 * @param months the amount of months, may be negative
 * @param days the amount of days, may be negative
 * @return the period of years, months and days, not null
 */
 public static Period of(int years, int months, int days) {
 return create(years, months, days);
 }

 //-----------------------------------------------------------------------
 /**
 * Obtains an instance of {@code Period} from a temporal amount.
 * <p>
 * This obtains a period based on the specified amount.
 * A {@code TemporalAmount} represents an amount of time, which may be
 * date-based or time-based, which this factory extracts to a {@code Period}.
 * <p>
 * The conversion loops around the set of units from the amount and uses
 * the {@link ChronoUnit#YEARS YEARS}, {@link ChronoUnit#MONTHS MONTHS}
 * and {@link ChronoUnit#DAYS DAYS} units to create a period.
 * If any other units are found then an exception is thrown.
 * <p>
 * If the amount is a {@code ChronoPeriod} then it must use the ISO chronology.
 *
 * @param amount the temporal amount to convert, not null
 * @return the equivalent period, not null
 * @throws DateTimeException if unable to convert to a {@code Period}
 * @throws ArithmeticException if the amount of years, months or days exceeds an int
 */
 public static Period from(TemporalAmount amount) {
 if (amount instanceof Period) {
 return (Period) amount;
 }
 if (amount instanceof ChronoPeriod) {
 if (IsoChronology.INSTANCE.equals(((ChronoPeriod) amount).getChronology()) == false) {
 throw new DateTimeException("Period requires ISO chronology: " + amount);
 }
 }
 Objects.requireNonNull(amount, "amount");
 int years = 0;
 int months = 0;
 int days = 0;
 for (TemporalUnit unit : amount.getUnits()) {
 long unitAmount = amount.get(unit);
 if (unit == ChronoUnit.YEARS) {
 years = Math.toIntExact(unitAmount);
 } else if (unit == ChronoUnit.MONTHS) {
 months = Math.toIntExact(unitAmount);
 } else if (unit == ChronoUnit.DAYS) {
 days = Math.toIntExact(unitAmount);
 } else {
 throw new DateTimeException("Unit must be Years, Months or Days, but was " + unit);
 }
 }
 return create(years, months, days);
 }

 //-----------------------------------------------------------------------
 /**
 * Obtains a {@code Period} from a text string such as {@code PnYnMnD}.
 * <p>
 * This will parse the string produced by {@code toString()} which is
 * based on the ISO-8601 period formats {@code PnYnMnD} and {@code PnW}.
 * <p>
 * The string starts with an optional sign, denoted by the ASCII negative
 * or positive symbol. If negative, the whole period is negated.
 * The ASCII letter "P" is next in upper or lower case.
 * There are then four sections, each consisting of a number and a suffix.
 * At least one of the four sections must be present.
 * The sections have suffixes in ASCII of "Y", "M", "W" and "D" for
 * years, months, weeks and days, accepted in upper or lower case.
 * The suffixes must occur in order.
 * The number part of each section must consist of ASCII digits.
 * The number may be prefixed by the ASCII negative or positive symbol.
 * The number must parse to an {@code int}.
 * <p>
 * The leading plus/minus sign, and negative values for other units are
 * not part of the ISO-8601 standard. In addition, ISO-8601 does not
 * permit mixing between the {@code PnYnMnD} and {@code PnW} formats.
 * Any week-based input is multiplied by 7 and treated as a number of days.
 * <p>
 * For example, the following are valid inputs:
 * <pre>
 * "P2Y" -- Period.ofYears(2)
 * "P3M" -- Period.ofMonths(3)
 * "P4W" -- Period.ofWeeks(4)
 * "P5D" -- Period.ofDays(5)
 * "P1Y2M3D" -- Period.of(1, 2, 3)
 * "P1Y2M3W4D" -- Period.of(1, 2, 25)
 * "P-1Y2M" -- Period.of(-1, 2, 0)
 * "-P1Y2M" -- Period.of(-1, -2, 0)
 * </pre>
 *
 * @param text the text to parse, not null
 * @return the parsed period, not null
 * @throws DateTimeParseException if the text cannot be parsed to a period
 */
 public static Period parse(CharSequence text) {
 Objects.requireNonNull(text, "text");
 Matcher matcher = PATTERN.matcher(text);
 if (matcher.matches()) {
 int negate = ("-".equals(matcher.group(1)) ? -1 : 1);
 String yearMatch = matcher.group(2);
 String monthMatch = matcher.group(3);
 String weekMatch = matcher.group(4);
 String dayMatch = matcher.group(5);
 if (yearMatch != null || monthMatch != null || dayMatch != null || weekMatch != null) {
 try {
 int years = parseNumber(text, yearMatch, negate);
 int months = parseNumber(text, monthMatch, negate);
 int weeks = parseNumber(text, weekMatch, negate);
 int days = parseNumber(text, dayMatch, negate);
 days = Math.addExact(days, Math.multiplyExact(weeks, 7));
 return create(years, months, days);
 } catch (NumberFormatException ex) {
 throw new DateTimeParseException("Text cannot be parsed to a Period", text, 0, ex);
 }
 }
 }
 throw new DateTimeParseException("Text cannot be parsed to a Period", text, 0);
 }

 private static int parseNumber(CharSequence text, String str, int negate) {
 if (str == null) {
 return 0;
 }
 int val = Integer.parseInt(str);
 try {
 return Math.multiplyExact(val, negate);
 } catch (ArithmeticException ex) {
 throw new DateTimeParseException("Text cannot be parsed to a Period", text, 0, ex);
 }
 }

 //-----------------------------------------------------------------------
 /**
 * Obtains a {@code Period} consisting of the number of years, months,
 * and days between two dates.
 * <p>
 * The start date is included, but the end date is not.
 * The period is calculated by removing complete months, then calculating
 * the remaining number of days, adjusting to ensure that both have the same sign.
 * The number of months is then split into years and months based on a 12 month year.
 * A month is considered if the end day-of-month is greater than or equal to the start day-of-month.
 * For example, from {@code 2010年01月15日} to {@code 2011年03月18日} is one year, two months and three days.
 * <p>
 * The result of this method can be a negative period if the end is before the start.
 * The negative sign will be the same in each of year, month and day.
 *
 * @param startDateInclusive the start date, inclusive, not null
 * @param endDateExclusive the end date, exclusive, not null
 * @return the period between this date and the end date, not null
 * @see ChronoLocalDate#until(ChronoLocalDate)
 */
 public static Period between(LocalDate startDateInclusive, LocalDate endDateExclusive) {
 return startDateInclusive.until(endDateExclusive);
 }

 //-----------------------------------------------------------------------
 /**
 * Creates an instance.
 *
 * @param years the amount
 * @param months the amount
 * @param days the amount
 */
 private static Period create(int years, int months, int days) {
 if ((years | months | days) == 0) {
 return ZERO;
 }
 return new Period(years, months, days);
 }

 /**
 * Constructor.
 *
 * @param years the amount
 * @param months the amount
 * @param days the amount
 */
 private Period(int years, int months, int days) {
 this.years = years;
 this.months = months;
 this.days = days;
 }

 //-----------------------------------------------------------------------
 /**
 * Gets the value of the requested unit.
 * <p>
 * This returns a value for each of the three supported units,
 * {@link ChronoUnit#YEARS YEARS}, {@link ChronoUnit#MONTHS MONTHS} and
 * {@link ChronoUnit#DAYS DAYS}.
 * All other units throw an exception.
 *
 * @param unit the {@code TemporalUnit} for which to return the value
 * @return the long value of the unit
 * @throws DateTimeException if the unit is not supported
 * @throws UnsupportedTemporalTypeException if the unit is not supported
 */
 @Override
 public long get(TemporalUnit unit) {
 if (unit == ChronoUnit.YEARS) {
 return getYears();
 } else if (unit == ChronoUnit.MONTHS) {
 return getMonths();
 } else if (unit == ChronoUnit.DAYS) {
 return getDays();
 } else {
 throw new UnsupportedTemporalTypeException("Unsupported unit: " + unit);
 }
 }

 /**
 * Gets the set of units supported by this period.
 * <p>
 * The supported units are {@link ChronoUnit#YEARS YEARS},
 * {@link ChronoUnit#MONTHS MONTHS} and {@link ChronoUnit#DAYS DAYS}.
 * They are returned in the order years, months, days.
 * <p>
 * This set can be used in conjunction with {@link #get(TemporalUnit)}
 * to access the entire state of the period.
 *
 * @return a list containing the years, months and days units, not null
 */
 @Override
 public List<TemporalUnit> getUnits() {
 return SUPPORTED_UNITS;
 }

 /**
 * Gets the chronology of this period, which is the ISO calendar system.
 * <p>
 * The {@code Chronology} represents the calendar system in use.
 * The ISO-8601 calendar system is the modern civil calendar system used today
 * in most of the world. It is equivalent to the proleptic Gregorian calendar
 * system, in which today's rules for leap years are applied for all time.
 *
 * @return the ISO chronology, not null
 */
 @Override
 public IsoChronology getChronology() {
 return IsoChronology.INSTANCE;
 }

 //-----------------------------------------------------------------------
 /**
 * Checks if all three units of this period are zero.
 * <p>
 * A zero period has the value zero for the years, months and days units.
 *
 * @return true if this period is zero-length
 */
 public boolean isZero() {
 return (this == ZERO);
 }

 /**
 * Checks if any of the three units of this period are negative.
 * <p>
 * This checks whether the years, months or days units are less than zero.
 *
 * @return true if any unit of this period is negative
 */
 public boolean isNegative() {
 return years < 0 || months < 0 || days < 0;
 }

 //-----------------------------------------------------------------------
 /**
 * Gets the amount of years of this period.
 * <p>
 * This returns the years unit.
 * <p>
 * The months unit is not automatically normalized with the years unit.
 * This means that a period of "15 months" is different to a period
 * of "1 year and 3 months".
 *
 * @return the amount of years of this period, may be negative
 */
 public int getYears() {
 return years;
 }

 /**
 * Gets the amount of months of this period.
 * <p>
 * This returns the months unit.
 * <p>
 * The months unit is not automatically normalized with the years unit.
 * This means that a period of "15 months" is different to a period
 * of "1 year and 3 months".
 *
 * @return the amount of months of this period, may be negative
 */
 public int getMonths() {
 return months;
 }

 /**
 * Gets the amount of days of this period.
 * <p>
 * This returns the days unit.
 *
 * @return the amount of days of this period, may be negative
 */
 public int getDays() {
 return days;
 }

 //-----------------------------------------------------------------------
 /**
 * Returns a copy of this period with the specified amount of years.
 * <p>
 * This sets the amount of the years unit in a copy of this period.
 * The months and days units are unaffected.
 * <p>
 * The months unit is not automatically normalized with the years unit.
 * This means that a period of "15 months" is different to a period
 * of "1 year and 3 months".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param years the years to represent, may be negative
 * @return a {@code Period} based on this period with the requested years, not null
 */
 public Period withYears(int years) {
 if (years == this.years) {
 return this;
 }
 return create(years, months, days);
 }

 /**
 * Returns a copy of this period with the specified amount of months.
 * <p>
 * This sets the amount of the months unit in a copy of this period.
 * The years and days units are unaffected.
 * <p>
 * The months unit is not automatically normalized with the years unit.
 * This means that a period of "15 months" is different to a period
 * of "1 year and 3 months".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param months the months to represent, may be negative
 * @return a {@code Period} based on this period with the requested months, not null
 */
 public Period withMonths(int months) {
 if (months == this.months) {
 return this;
 }
 return create(years, months, days);
 }

 /**
 * Returns a copy of this period with the specified amount of days.
 * <p>
 * This sets the amount of the days unit in a copy of this period.
 * The years and months units are unaffected.
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param days the days to represent, may be negative
 * @return a {@code Period} based on this period with the requested days, not null
 */
 public Period withDays(int days) {
 if (days == this.days) {
 return this;
 }
 return create(years, months, days);
 }

 //-----------------------------------------------------------------------
 /**
 * Returns a copy of this period with the specified period added.
 * <p>
 * This operates separately on the years, months and days.
 * No normalization is performed.
 * <p>
 * For example, "1 year, 6 months and 3 days" plus "2 years, 2 months and 2 days"
 * returns "3 years, 8 months and 5 days".
 * <p>
 * The specified amount is typically an instance of {@code Period}.
 * Other types are interpreted using {@link Period#from(TemporalAmount)}.
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param amountToAdd the amount to add, not null
 * @return a {@code Period} based on this period with the requested period added, not null
 * @throws DateTimeException if the specified amount has a non-ISO chronology or
 * contains an invalid unit
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period plus(TemporalAmount amountToAdd) {
 Period isoAmount = Period.from(amountToAdd);
 return create(
 Math.addExact(years, isoAmount.years),
 Math.addExact(months, isoAmount.months),
 Math.addExact(days, isoAmount.days));
 }

 /**
 * Returns a copy of this period with the specified years added.
 * <p>
 * This adds the amount to the years unit in a copy of this period.
 * The months and days units are unaffected.
 * For example, "1 year, 6 months and 3 days" plus 2 years returns "3 years, 6 months and 3 days".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param yearsToAdd the years to add, positive or negative
 * @return a {@code Period} based on this period with the specified years added, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period plusYears(long yearsToAdd) {
 if (yearsToAdd == 0) {
 return this;
 }
 return create(Math.toIntExact(Math.addExact(years, yearsToAdd)), months, days);
 }

 /**
 * Returns a copy of this period with the specified months added.
 * <p>
 * This adds the amount to the months unit in a copy of this period.
 * The years and days units are unaffected.
 * For example, "1 year, 6 months and 3 days" plus 2 months returns "1 year, 8 months and 3 days".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param monthsToAdd the months to add, positive or negative
 * @return a {@code Period} based on this period with the specified months added, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period plusMonths(long monthsToAdd) {
 if (monthsToAdd == 0) {
 return this;
 }
 return create(years, Math.toIntExact(Math.addExact(months, monthsToAdd)), days);
 }

 /**
 * Returns a copy of this period with the specified days added.
 * <p>
 * This adds the amount to the days unit in a copy of this period.
 * The years and months units are unaffected.
 * For example, "1 year, 6 months and 3 days" plus 2 days returns "1 year, 6 months and 5 days".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param daysToAdd the days to add, positive or negative
 * @return a {@code Period} based on this period with the specified days added, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period plusDays(long daysToAdd) {
 if (daysToAdd == 0) {
 return this;
 }
 return create(years, months, Math.toIntExact(Math.addExact(days, daysToAdd)));
 }

 //-----------------------------------------------------------------------
 /**
 * Returns a copy of this period with the specified period subtracted.
 * <p>
 * This operates separately on the years, months and days.
 * No normalization is performed.
 * <p>
 * For example, "1 year, 6 months and 3 days" minus "2 years, 2 months and 2 days"
 * returns "-1 years, 4 months and 1 day".
 * <p>
 * The specified amount is typically an instance of {@code Period}.
 * Other types are interpreted using {@link Period#from(TemporalAmount)}.
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param amountToSubtract the amount to subtract, not null
 * @return a {@code Period} based on this period with the requested period subtracted, not null
 * @throws DateTimeException if the specified amount has a non-ISO chronology or
 * contains an invalid unit
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period minus(TemporalAmount amountToSubtract) {
 Period isoAmount = Period.from(amountToSubtract);
 return create(
 Math.subtractExact(years, isoAmount.years),
 Math.subtractExact(months, isoAmount.months),
 Math.subtractExact(days, isoAmount.days));
 }

 /**
 * Returns a copy of this period with the specified years subtracted.
 * <p>
 * This subtracts the amount from the years unit in a copy of this period.
 * The months and days units are unaffected.
 * For example, "1 year, 6 months and 3 days" minus 2 years returns "-1 years, 6 months and 3 days".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param yearsToSubtract the years to subtract, positive or negative
 * @return a {@code Period} based on this period with the specified years subtracted, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period minusYears(long yearsToSubtract) {
 return (yearsToSubtract == Long.MIN_VALUE ? plusYears(Long.MAX_VALUE).plusYears(1) : plusYears(-yearsToSubtract));
 }

 /**
 * Returns a copy of this period with the specified months subtracted.
 * <p>
 * This subtracts the amount from the months unit in a copy of this period.
 * The years and days units are unaffected.
 * For example, "1 year, 6 months and 3 days" minus 2 months returns "1 year, 4 months and 3 days".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param monthsToSubtract the years to subtract, positive or negative
 * @return a {@code Period} based on this period with the specified months subtracted, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period minusMonths(long monthsToSubtract) {
 return (monthsToSubtract == Long.MIN_VALUE ? plusMonths(Long.MAX_VALUE).plusMonths(1) : plusMonths(-monthsToSubtract));
 }

 /**
 * Returns a copy of this period with the specified days subtracted.
 * <p>
 * This subtracts the amount from the days unit in a copy of this period.
 * The years and months units are unaffected.
 * For example, "1 year, 6 months and 3 days" minus 2 days returns "1 year, 6 months and 1 day".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param daysToSubtract the months to subtract, positive or negative
 * @return a {@code Period} based on this period with the specified days subtracted, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period minusDays(long daysToSubtract) {
 return (daysToSubtract == Long.MIN_VALUE ? plusDays(Long.MAX_VALUE).plusDays(1) : plusDays(-daysToSubtract));
 }

 //-----------------------------------------------------------------------
 /**
 * Returns a new instance with each element in this period multiplied
 * by the specified scalar.
 * <p>
 * This returns a period with each of the years, months and days units
 * individually multiplied.
 * For example, a period of "2 years, -3 months and 4 days" multiplied by
 * 3 will return "6 years, -9 months and 12 days".
 * No normalization is performed.
 *
 * @param scalar the scalar to multiply by, not null
 * @return a {@code Period} based on this period with the amounts multiplied by the scalar, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period multipliedBy(int scalar) {
 if (this == ZERO || scalar == 1) {
 return this;
 }
 return create(
 Math.multiplyExact(years, scalar),
 Math.multiplyExact(months, scalar),
 Math.multiplyExact(days, scalar));
 }

 /**
 * Returns a new instance with each amount in this period negated.
 * <p>
 * This returns a period with each of the years, months and days units
 * individually negated.
 * For example, a period of "2 years, -3 months and 4 days" will be
 * negated to "-2 years, 3 months and -4 days".
 * No normalization is performed.
 *
 * @return a {@code Period} based on this period with the amounts negated, not null
 * @throws ArithmeticException if numeric overflow occurs, which only happens if
 * one of the units has the value {@code Long.MIN_VALUE}
 */
 public Period negated() {
 return multipliedBy(-1);
 }

 //-----------------------------------------------------------------------
 /**
 * Returns a copy of this period with the years and months normalized.
 * <p>
 * This normalizes the years and months units, leaving the days unit unchanged.
 * The months unit is adjusted to have an absolute value less than 11,
 * with the years unit being adjusted to compensate. For example, a period of
 * "1 Year and 15 months" will be normalized to "2 years and 3 months".
 * <p>
 * The sign of the years and months units will be the same after normalization.
 * For example, a period of "1 year and -25 months" will be normalized to
 * "-1 year and -1 month".
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @return a {@code Period} based on this period with excess months normalized to years, not null
 * @throws ArithmeticException if numeric overflow occurs
 */
 public Period normalized() {
 long totalMonths = toTotalMonths();
 long splitYears = totalMonths / 12;
 int splitMonths = (int) (totalMonths % 12); // no overflow
 if (splitYears == years && splitMonths == months) {
 return this;
 }
 return create(Math.toIntExact(splitYears), splitMonths, days);
 }

 /**
 * Gets the total number of months in this period.
 * <p>
 * This returns the total number of months in the period by multiplying the
 * number of years by 12 and adding the number of months.
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @return the total number of months in the period, may be negative
 */
 public long toTotalMonths() {
 return years * 12L + months; // no overflow
 }

 //-------------------------------------------------------------------------
 /**
 * Adds this period to the specified temporal object.
 * <p>
 * This returns a temporal object of the same observable type as the input
 * with this period added.
 * If the temporal has a chronology, it must be the ISO chronology.
 * <p>
 * In most cases, it is clearer to reverse the calling pattern by using
 * {@link Temporal#plus(TemporalAmount)}.
 * <pre>
 * // these two lines are equivalent, but the second approach is recommended
 * dateTime = thisPeriod.addTo(dateTime);
 * dateTime = dateTime.plus(thisPeriod);
 * </pre>
 * <p>
 * The calculation operates as follows.
 * First, the chronology of the temporal is checked to ensure it is ISO chronology or null.
 * Second, if the months are zero, the years are added if non-zero, otherwise
 * the combination of years and months is added if non-zero.
 * Finally, any days are added.
 * <p>
 * This approach ensures that a partial period can be added to a partial date.
 * For example, a period of years and/or months can be added to a {@code YearMonth},
 * but a period including days cannot.
 * The approach also adds years and months together when necessary, which ensures
 * correct behaviour at the end of the month.
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param temporal the temporal object to adjust, not null
 * @return an object of the same type with the adjustment made, not null
 * @throws DateTimeException if unable to add
 * @throws ArithmeticException if numeric overflow occurs
 */
 @Override
 public Temporal addTo(Temporal temporal) {
 validateChrono(temporal);
 if (months == 0) {
 if (years != 0) {
 temporal = temporal.plus(years, YEARS);
 }
 } else {
 long totalMonths = toTotalMonths();
 if (totalMonths != 0) {
 temporal = temporal.plus(totalMonths, MONTHS);
 }
 }
 if (days != 0) {
 temporal = temporal.plus(days, DAYS);
 }
 return temporal;
 }

 /**
 * Subtracts this period from the specified temporal object.
 * <p>
 * This returns a temporal object of the same observable type as the input
 * with this period subtracted.
 * If the temporal has a chronology, it must be the ISO chronology.
 * <p>
 * In most cases, it is clearer to reverse the calling pattern by using
 * {@link Temporal#minus(TemporalAmount)}.
 * <pre>
 * // these two lines are equivalent, but the second approach is recommended
 * dateTime = thisPeriod.subtractFrom(dateTime);
 * dateTime = dateTime.minus(thisPeriod);
 * </pre>
 * <p>
 * The calculation operates as follows.
 * First, the chronology of the temporal is checked to ensure it is ISO chronology or null.
 * Second, if the months are zero, the years are subtracted if non-zero, otherwise
 * the combination of years and months is subtracted if non-zero.
 * Finally, any days are subtracted.
 * <p>
 * This approach ensures that a partial period can be subtracted from a partial date.
 * For example, a period of years and/or months can be subtracted from a {@code YearMonth},
 * but a period including days cannot.
 * The approach also subtracts years and months together when necessary, which ensures
 * correct behaviour at the end of the month.
 * <p>
 * This instance is immutable and unaffected by this method call.
 *
 * @param temporal the temporal object to adjust, not null
 * @return an object of the same type with the adjustment made, not null
 * @throws DateTimeException if unable to subtract
 * @throws ArithmeticException if numeric overflow occurs
 */
 @Override
 public Temporal subtractFrom(Temporal temporal) {
 validateChrono(temporal);
 if (months == 0) {
 if (years != 0) {
 temporal = temporal.minus(years, YEARS);
 }
 } else {
 long totalMonths = toTotalMonths();
 if (totalMonths != 0) {
 temporal = temporal.minus(totalMonths, MONTHS);
 }
 }
 if (days != 0) {
 temporal = temporal.minus(days, DAYS);
 }
 return temporal;
 }

 /**
 * Validates that the temporal has the correct chronology.
 */
 private void validateChrono(TemporalAccessor temporal) {
 Objects.requireNonNull(temporal, "temporal");
 Chronology temporalChrono = temporal.query(TemporalQueries.chronology());
 if (temporalChrono != null && IsoChronology.INSTANCE.equals(temporalChrono) == false) {
 throw new DateTimeException("Chronology mismatch, expected: ISO, actual: " + temporalChrono.getId());
 }
 }

 //-----------------------------------------------------------------------
 /**
 * Checks if this period is equal to another period.
 * <p>
 * The comparison is based on the type {@code Period} and each of the three amounts.
 * To be equal, the years, months and days units must be individually equal.
 * Note that this means that a period of "15 Months" is not equal to a period
 * of "1 Year and 3 Months".
 *
 * @param obj the object to check, null returns false
 * @return true if this is equal to the other period
 */
 @Override
 public boolean equals(Object obj) {
 if (this == obj) {
 return true;
 }
 if (obj instanceof Period) {
 Period other = (Period) obj;
 return years == other.years &&
 months == other.months &&
 days == other.days;
 }
 return false;
 }

 /**
 * A hash code for this period.
 *
 * @return a suitable hash code
 */
 @Override
 public int hashCode() {
 return years + Integer.rotateLeft(months, 8) + Integer.rotateLeft(days, 16);
 }

 //-----------------------------------------------------------------------
 /**
 * Outputs this period as a {@code String}, such as {@code P6Y3M1D}.
 * <p>
 * The output will be in the ISO-8601 period format.
 * A zero period will be represented as zero days, 'P0D'.
 *
 * @return a string representation of this period, not null
 */
 @Override
 public String toString() {
 if (this == ZERO) {
 return "P0D";
 } else {
 StringBuilder buf = new StringBuilder();
 buf.append('P');
 if (years != 0) {
 buf.append(years).append('Y');
 }
 if (months != 0) {
 buf.append(months).append('M');
 }
 if (days != 0) {
 buf.append(days).append('D');
 }
 return buf.toString();
 }
 }

 //-----------------------------------------------------------------------
 /**
 * Writes the object using a
 * <a href="../../serialized-form.html#java.time.Ser">dedicated serialized form</a>.
 * @serialData
 * <pre>
 * out.writeByte(14); // identifies a Period
 * out.writeInt(years);
 * out.writeInt(months);
 * out.writeInt(days);
 * </pre>
 *
 * @return the instance of {@code Ser}, not null
 */
 private Object writeReplace() {
 return new Ser(Ser.PERIOD_TYPE, this);
 }

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

 void writeExternal(DataOutput out) throws IOException {
 out.writeInt(years);
 out.writeInt(months);
 out.writeInt(days);
 }

 static Period readExternal(DataInput in) throws IOException {
 int years = in.readInt();
 int months = in.readInt();
 int days = in.readInt();
 return Period.of(years, months, days);
 }

}