/**
 * Copyright (C) 2018 Adrien Hopkins
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Affero General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program.  If not, see <https://www.gnu.org/licenses/>.
 */
package sevenUnits.unit;

import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigDecimal;
import java.nio.file.Files;
import java.nio.file.Path;
import java.util.AbstractSet;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Scanner;
import java.util.Set;
import java.util.function.BiFunction;
import java.util.function.Function;
import java.util.function.Predicate;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

import sevenUnits.utils.ConditionalExistenceCollections;
import sevenUnits.utils.DecimalComparison;
import sevenUnits.utils.ExpressionParser;
import sevenUnits.utils.ObjectProduct;
import sevenUnits.utils.UncertainDouble;

/**
 * A database of units, prefixes and dimensions, and their names.
 * 
 * @author Adrien Hopkins
 * @since 2019-01-07
 * @since v0.1.0
 */
public final class UnitDatabase {
	/**
	 * A map for units that allows the use of prefixes.
	 * <p>
	 * As this map implementation is intended to be used as a sort of "augmented
	 * view" of a unit and prefix map, it is unmodifiable but instead reflects
	 * the changes to the maps passed into it. Do not edit this map, instead edit
	 * the maps that were passed in during construction.
	 * </p>
	 * <p>
	 * The rules for applying prefixes onto units are the following:
	 * <ul>
	 * <li>Prefixes can only be applied to linear units.</li>
	 * <li>Before attempting to search for prefixes in a unit name, this map will
	 * first search for a unit name. So, if there are two units, "B" and "AB",
	 * and a prefix "A", this map will favour the unit "AB" over the unit "B"
	 * with the prefix "A", even though they have the same string.</li>
	 * <li>Longer prefixes are preferred to shorter prefixes. So, if you have
	 * units "BC" and "C", and prefixes "AB" and "A", inputting "ABC" will return
	 * the unit "C" with the prefix "AB", not "BC" with the prefix "A".</li>
	 * </ul>
	 * </p>
	 * <p>
	 * This map is infinite in size if there is at least one unit and at least
	 * one prefix. If it is infinite, some operations that only work with finite
	 * collections, like converting name/entry sets to arrays, will throw an
	 * {@code IllegalStateException}.
	 * </p>
	 * <p>
	 * Because of ambiguities between prefixes (i.e. kilokilo = mega),
	 * {@link #containsValue} and {@link #values()} currently ignore prefixes.
	 * </p>
	 * 
	 * @author Adrien Hopkins
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	private static final class PrefixedUnitMap implements Map<String, Unit> {
		/**
		 * The class used for entry sets.
		 * 
		 * <p>
		 * If the map that created this set is infinite in size (has at least one
		 * unit and at least one prefix), this set is infinite as well. If this
		 * set is infinite in size, {@link #toArray} will fail with a
		 * {@code IllegalStateException} instead of creating an infinite-sized
		 * array.
		 * </p>
		 * 
		 * @author Adrien Hopkins
		 * @since 2019-04-13
		 * @since v0.2.0
		 */
		private static final class PrefixedUnitEntrySet
				extends AbstractSet<Map.Entry<String, Unit>> {
			/**
			 * The entry for this set.
			 * 
			 * @author Adrien Hopkins
			 * @since 2019-04-14
			 * @since v0.2.0
			 */
			private static final class PrefixedUnitEntry
					implements Entry<String, Unit> {
				private final String key;
				private final Unit value;
				
				/**
				 * Creates the {@code PrefixedUnitEntry}.
				 * 
				 * @param key   key
				 * @param value value
				 * @since 2019-04-14
				 * @since v0.2.0
				 */
				public PrefixedUnitEntry(final String key, final Unit value) {
					this.key = key;
					this.value = value;
				}
				
				/**
				 * @since 2019-05-03
				 */
				@Override
				public boolean equals(final Object o) {
					if (!(o instanceof Map.Entry))
						return false;
					final Map.Entry<?, ?> other = (Map.Entry<?, ?>) o;
					return Objects.equals(this.getKey(), other.getKey())
							&& Objects.equals(this.getValue(), other.getValue());
				}
				
				@Override
				public String getKey() {
					return this.key;
				}
				
				@Override
				public Unit getValue() {
					return this.value;
				}
				
				/**
				 * @since 2019-05-03
				 */
				@Override
				public int hashCode() {
					return (this.getKey() == null ? 0 : this.getKey().hashCode())
							^ (this.getValue() == null ? 0
									: this.getValue().hashCode());
				}
				
				@Override
				public Unit setValue(final Unit value) {
					throw new UnsupportedOperationException(
							"Cannot set value in an immutable entry");
				}
				
				/**
				 * Returns a string representation of the entry. The format of the
				 * string is the string representation of the key, then the equals
				 * ({@code =}) character, then the string representation of the
				 * value.
				 * 
				 * @since 2019-05-03
				 */
				@Override
				public String toString() {
					return this.getKey() + "=" + this.getValue();
				}
			}
			
			/**
			 * An iterator that iterates over the units of a
			 * {@code PrefixedUnitNameSet}.
			 * 
			 * @author Adrien Hopkins
			 * @since 2019-04-14
			 * @since v0.2.0
			 */
			private static final class PrefixedUnitEntryIterator
					implements Iterator<Entry<String, Unit>> {
				// position in the unit list
				private int unitNamePosition = 0;
				// the indices of the prefixes attached to the current unit
				private final List<Integer> prefixCoordinates = new ArrayList<>();
				
				// values from the unit entry set
				private final Map<String, Unit> map;
				private transient final List<String> unitNames;
				private transient final List<String> prefixNames;
				
				/**
				 * Creates the
				 * {@code UnitsDatabase.PrefixedUnitMap.PrefixedUnitNameSet.PrefixedUnitNameIterator}.
				 * 
				 * @since 2019-04-14
				 * @since v0.2.0
				 */
				public PrefixedUnitEntryIterator(final PrefixedUnitMap map) {
					this.map = map;
					this.unitNames = new ArrayList<>(map.units.keySet());
					this.prefixNames = new ArrayList<>(map.prefixes.keySet());
				}
				
				/**
				 * @return current unit name
				 * @since 2019-04-14
				 * @since v0.2.0
				 */
				private String getCurrentUnitName() {
					final StringBuilder unitName = new StringBuilder();
					for (final int i : this.prefixCoordinates) {
						unitName.append(this.prefixNames.get(i));
					}
					unitName.append(this.unitNames.get(this.unitNamePosition));
					
					return unitName.toString();
				}
				
				@Override
				public boolean hasNext() {
					if (this.unitNames.isEmpty())
						return false;
					else {
						if (this.prefixNames.isEmpty())
							return this.unitNamePosition >= this.unitNames.size() - 1;
						else
							return true;
					}
				}
				
				/**
				 * Changes this iterator's position to the next available one.
				 * 
				 * @since 2019-04-14
				 * @since v0.2.0
				 */
				private void incrementPosition() {
					this.unitNamePosition++;
					
					if (this.unitNamePosition >= this.unitNames.size()) {
						// we have used all of our units, go to a different prefix
						this.unitNamePosition = 0;
						
						// if the prefix coordinates are empty, then set it to [0]
						if (this.prefixCoordinates.isEmpty()) {
							this.prefixCoordinates.add(0, 0);
						} else {
							// get the prefix coordinate to increment, then increment
							int i = this.prefixCoordinates.size() - 1;
							this.prefixCoordinates.set(i,
									this.prefixCoordinates.get(i) + 1);
							
							// fix any carrying errors
							while (i >= 0 && this.prefixCoordinates
									.get(i) >= this.prefixNames.size()) {
								// carry over
								this.prefixCoordinates.set(i--, 0); // null and
																				// decrement at the
																				// same time
								
								if (i < 0) { // we need to add a new coordinate
									this.prefixCoordinates.add(0, 0);
								} else { // increment an existing one
									this.prefixCoordinates.set(i,
											this.prefixCoordinates.get(i) + 1);
								}
							}
						}
					}
				}
				
				@Override
				public Entry<String, Unit> next() {
					// get next element
					final Entry<String, Unit> nextEntry = this.peek();
					
					// iterate to next position
					this.incrementPosition();
					
					return nextEntry;
				}
				
				/**
				 * @return the next element in the iterator, without iterating over
				 *         it
				 * @since 2019-05-03
				 */
				private Entry<String, Unit> peek() {
					if (!this.hasNext())
						throw new NoSuchElementException("No units left!");
						
					// if I have prefixes, ensure I'm not using a nonlinear unit
					// since all of the unprefixed stuff is done, just remove
					// nonlinear units
					if (!this.prefixCoordinates.isEmpty()) {
						while (this.unitNamePosition < this.unitNames.size()
								&& !(this.map.get(this.unitNames.get(
										this.unitNamePosition)) instanceof LinearUnit)) {
							this.unitNames.remove(this.unitNamePosition);
						}
					}
					
					final String nextName = this.getCurrentUnitName();
					
					return new PrefixedUnitEntry(nextName, this.map.get(nextName));
				}
				
				/**
				 * Returns a string representation of the object. The exact details
				 * of the representation are unspecified and subject to change.
				 * 
				 * @since 2019-05-03
				 */
				@Override
				public String toString() {
					return String.format(
							"Iterator iterating over name-unit entries; next value is \"%s\"",
							this.peek());
				}
			}
			
			// the map that created this set
			private final PrefixedUnitMap map;
			
			/**
			 * Creates the {@code PrefixedUnitNameSet}.
			 * 
			 * @param map map that created this set
			 * @since 2019-04-13
			 * @since v0.2.0
			 */
			public PrefixedUnitEntrySet(final PrefixedUnitMap map) {
				this.map = map;
			}
			
			@Override
			public boolean add(final Map.Entry<String, Unit> e) {
				throw new UnsupportedOperationException(
						"Cannot add to an immutable set");
			}
			
			@Override
			public boolean addAll(
					final Collection<? extends Map.Entry<String, Unit>> c) {
				throw new UnsupportedOperationException(
						"Cannot add to an immutable set");
			}
			
			@Override
			public void clear() {
				throw new UnsupportedOperationException(
						"Cannot clear an immutable set");
			}
			
			@Override
			public boolean contains(final Object o) {
				// get the entry
				final Entry<String, Unit> entry;
				
				try {
					// This is OK because I'm in a try-catch block, catching the
					// exact exception that would be thrown.
					@SuppressWarnings("unchecked")
					final Entry<String, Unit> tempEntry = (Entry<String, Unit>) o;
					entry = tempEntry;
				} catch (final ClassCastException e) {
					throw new IllegalArgumentException(
							"Attempted to test for an entry using a non-entry.");
				}
				
				return this.map.containsKey(entry.getKey())
						&& this.map.get(entry.getKey()).equals(entry.getValue());
			}
			
			@Override
			public boolean containsAll(final Collection<?> c) {
				for (final Object o : c)
					if (!this.contains(o))
						return false;
				return true;
			}
			
			@Override
			public boolean isEmpty() {
				return this.map.isEmpty();
			}
			
			@Override
			public Iterator<Entry<String, Unit>> iterator() {
				return new PrefixedUnitEntryIterator(this.map);
			}
			
			@Override
			public boolean remove(final Object o) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public boolean removeAll(final Collection<?> c) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public boolean removeIf(
					final Predicate<? super Entry<String, Unit>> filter) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public boolean retainAll(final Collection<?> c) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public int size() {
				if (this.map.units.isEmpty())
					return 0;
				else {
					if (this.map.prefixes.isEmpty())
						return this.map.units.size();
					else
						// infinite set
						return Integer.MAX_VALUE;
				}
			}
			
			/**
			 * @throws IllegalStateException if the set is infinite in size
			 */
			@Override
			public Object[] toArray() {
				if (this.map.units.isEmpty() || this.map.prefixes.isEmpty())
					return super.toArray();
				else
					// infinite set
					throw new IllegalStateException(
							"Cannot make an infinite set into an array.");
			}
			
			/**
			 * @throws IllegalStateException if the set is infinite in size
			 */
			@Override
			public <T> T[] toArray(final T[] a) {
				if (this.map.units.isEmpty() || this.map.prefixes.isEmpty())
					return super.toArray(a);
				else
					// infinite set
					throw new IllegalStateException(
							"Cannot make an infinite set into an array.");
			}
			
			@Override
			public String toString() {
				if (this.map.units.isEmpty() || this.map.prefixes.isEmpty())
					return super.toString();
				else
					return String.format(
							"Infinite set of name-unit entries created from units %s and prefixes %s",
							this.map.units, this.map.prefixes);
			}
		}
		
		/**
		 * The class used for unit name sets.
		 * 
		 * <p>
		 * If the map that created this set is infinite in size (has at least one
		 * unit and at least one prefix), this set is infinite as well. If this
		 * set is infinite in size, {@link #toArray} will fail with a
		 * {@code IllegalStateException} instead of creating an infinite-sized
		 * array.
		 * </p>
		 * 
		 * @author Adrien Hopkins
		 * @since 2019-04-13
		 * @since v0.2.0
		 */
		private static final class PrefixedUnitNameSet
				extends AbstractSet<String> {
			/**
			 * An iterator that iterates over the units of a
			 * {@code PrefixedUnitNameSet}.
			 * 
			 * @author Adrien Hopkins
			 * @since 2019-04-14
			 * @since v0.2.0
			 */
			private static final class PrefixedUnitNameIterator
					implements Iterator<String> {
				// position in the unit list
				private int unitNamePosition = 0;
				// the indices of the prefixes attached to the current unit
				private final List<Integer> prefixCoordinates = new ArrayList<>();
				
				// values from the unit name set
				private final Map<String, Unit> map;
				private transient final List<String> unitNames;
				private transient final List<String> prefixNames;
				
				/**
				 * Creates the
				 * {@code UnitsDatabase.PrefixedUnitMap.PrefixedUnitNameSet.PrefixedUnitNameIterator}.
				 * 
				 * @since 2019-04-14
				 * @since v0.2.0
				 */
				public PrefixedUnitNameIterator(final PrefixedUnitMap map) {
					this.map = map;
					this.unitNames = new ArrayList<>(map.units.keySet());
					this.prefixNames = new ArrayList<>(map.prefixes.keySet());
				}
				
				/**
				 * @return current unit name
				 * @since 2019-04-14
				 * @since v0.2.0
				 */
				private String getCurrentUnitName() {
					final StringBuilder unitName = new StringBuilder();
					for (final int i : this.prefixCoordinates) {
						unitName.append(this.prefixNames.get(i));
					}
					unitName.append(this.unitNames.get(this.unitNamePosition));
					
					return unitName.toString();
				}
				
				@Override
				public boolean hasNext() {
					if (this.unitNames.isEmpty())
						return false;
					else {
						if (this.prefixNames.isEmpty())
							return this.unitNamePosition >= this.unitNames.size() - 1;
						else
							return true;
					}
				}
				
				/**
				 * Changes this iterator's position to the next available one.
				 * 
				 * @since 2019-04-14
				 * @since v0.2.0
				 */
				private void incrementPosition() {
					this.unitNamePosition++;
					
					if (this.unitNamePosition >= this.unitNames.size()) {
						// we have used all of our units, go to a different prefix
						this.unitNamePosition = 0;
						
						// if the prefix coordinates are empty, then set it to [0]
						if (this.prefixCoordinates.isEmpty()) {
							this.prefixCoordinates.add(0, 0);
						} else {
							// get the prefix coordinate to increment, then increment
							int i = this.prefixCoordinates.size() - 1;
							this.prefixCoordinates.set(i,
									this.prefixCoordinates.get(i) + 1);
							
							// fix any carrying errors
							while (i >= 0 && this.prefixCoordinates
									.get(i) >= this.prefixNames.size()) {
								// carry over
								this.prefixCoordinates.set(i--, 0); // null and
																				// decrement at the
																				// same time
								
								if (i < 0) { // we need to add a new coordinate
									this.prefixCoordinates.add(0, 0);
								} else { // increment an existing one
									this.prefixCoordinates.set(i,
											this.prefixCoordinates.get(i) + 1);
								}
							}
						}
					}
				}
				
				@Override
				public String next() {
					final String nextName = this.peek();
					
					this.incrementPosition();
					
					return nextName;
				}
				
				/**
				 * @return the next element in the iterator, without iterating over
				 *         it
				 * @since 2019-05-03
				 */
				private String peek() {
					if (!this.hasNext())
						throw new NoSuchElementException("No units left!");
					// if I have prefixes, ensure I'm not using a nonlinear unit
					// since all of the unprefixed stuff is done, just remove
					// nonlinear units
					if (!this.prefixCoordinates.isEmpty()) {
						while (this.unitNamePosition < this.unitNames.size()
								&& !(this.map.get(this.unitNames.get(
										this.unitNamePosition)) instanceof LinearUnit)) {
							this.unitNames.remove(this.unitNamePosition);
						}
					}
					
					return this.getCurrentUnitName();
				}
				
				/**
				 * Returns a string representation of the object. The exact details
				 * of the representation are unspecified and subject to change.
				 * 
				 * @since 2019-05-03
				 */
				@Override
				public String toString() {
					return String.format(
							"Iterator iterating over unit names; next value is \"%s\"",
							this.peek());
				}
			}
			
			// the map that created this set
			private final PrefixedUnitMap map;
			
			/**
			 * Creates the {@code PrefixedUnitNameSet}.
			 * 
			 * @param map map that created this set
			 * @since 2019-04-13
			 * @since v0.2.0
			 */
			public PrefixedUnitNameSet(final PrefixedUnitMap map) {
				this.map = map;
			}
			
			@Override
			public boolean add(final String e) {
				throw new UnsupportedOperationException(
						"Cannot add to an immutable set");
			}
			
			@Override
			public boolean addAll(final Collection<? extends String> c) {
				throw new UnsupportedOperationException(
						"Cannot add to an immutable set");
			}
			
			@Override
			public void clear() {
				throw new UnsupportedOperationException(
						"Cannot clear an immutable set");
			}
			
			@Override
			public boolean contains(final Object o) {
				return this.map.containsKey(o);
			}
			
			@Override
			public boolean containsAll(final Collection<?> c) {
				for (final Object o : c)
					if (!this.contains(o))
						return false;
				return true;
			}
			
			@Override
			public boolean isEmpty() {
				return this.map.isEmpty();
			}
			
			@Override
			public Iterator<String> iterator() {
				return new PrefixedUnitNameIterator(this.map);
			}
			
			@Override
			public boolean remove(final Object o) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public boolean removeAll(final Collection<?> c) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public boolean removeIf(final Predicate<? super String> filter) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public boolean retainAll(final Collection<?> c) {
				throw new UnsupportedOperationException(
						"Cannot remove from an immutable set");
			}
			
			@Override
			public int size() {
				if (this.map.units.isEmpty())
					return 0;
				else {
					if (this.map.prefixes.isEmpty())
						return this.map.units.size();
					else
						// infinite set
						return Integer.MAX_VALUE;
				}
			}
			
			/**
			 * @throws IllegalStateException if the set is infinite in size
			 */
			@Override
			public Object[] toArray() {
				if (this.map.units.isEmpty() || this.map.prefixes.isEmpty())
					return super.toArray();
				else
					// infinite set
					throw new IllegalStateException(
							"Cannot make an infinite set into an array.");
				
			}
			
			/**
			 * @throws IllegalStateException if the set is infinite in size
			 */
			@Override
			public <T> T[] toArray(final T[] a) {
				if (this.map.units.isEmpty() || this.map.prefixes.isEmpty())
					return super.toArray(a);
				else
					// infinite set
					throw new IllegalStateException(
							"Cannot make an infinite set into an array.");
			}
			
			@Override
			public String toString() {
				if (this.map.units.isEmpty() || this.map.prefixes.isEmpty())
					return super.toString();
				else
					return String.format(
							"Infinite set of name-unit entries created from units %s and prefixes %s",
							this.map.units, this.map.prefixes);
			}
		}
		
		/**
		 * The units stored in this collection, without prefixes.
		 * 
		 * @since 2019-04-13
		 * @since v0.2.0
		 */
		private final Map<String, Unit> units;
		
		/**
		 * The available prefixes for use.
		 * 
		 * @since 2019-04-13
		 * @since v0.2.0
		 */
		private final Map<String, UnitPrefix> prefixes;
		
		// caches
		private transient Collection<Unit> values = null;
		private transient Set<String> keySet = null;
		private transient Set<Entry<String, Unit>> entrySet = null;
		
		/**
		 * Creates the {@code PrefixedUnitMap}.
		 * 
		 * @param units    map mapping unit names to units
		 * @param prefixes map mapping prefix names to prefixes
		 * @since 2019-04-13
		 * @since v0.2.0
		 */
		public PrefixedUnitMap(final Map<String, Unit> units,
				final Map<String, UnitPrefix> prefixes) {
			// I am making unmodifiable maps to ensure I don't accidentally make
			// changes.
			this.units = Collections.unmodifiableMap(units);
			this.prefixes = Collections.unmodifiableMap(prefixes);
		}
		
		@Override
		public void clear() {
			throw new UnsupportedOperationException(
					"Cannot clear an immutable map");
		}
		
		@Override
		public Unit compute(final String key,
				final BiFunction<? super String, ? super Unit, ? extends Unit> remappingFunction) {
			throw new UnsupportedOperationException(
					"Cannot edit an immutable map");
		}
		
		@Override
		public Unit computeIfAbsent(final String key,
				final Function<? super String, ? extends Unit> mappingFunction) {
			throw new UnsupportedOperationException(
					"Cannot edit an immutable map");
		}
		
		@Override
		public Unit computeIfPresent(final String key,
				final BiFunction<? super String, ? super Unit, ? extends Unit> remappingFunction) {
			throw new UnsupportedOperationException(
					"Cannot edit an immutable map");
		}
		
		@Override
		public boolean containsKey(final Object key) {
			// First, test if there is a unit with the key
			if (this.units.containsKey(key))
				return true;
			
			// Next, try to cast it to String
			if (!(key instanceof String))
				throw new IllegalArgumentException(
						"Attempted to test for a unit using a non-string name.");
			final String unitName = (String) key;
			
			// Then, look for the longest prefix that is attached to a valid unit
			String longestPrefix = null;
			int longestLength = 0;
			
			for (final String prefixName : this.prefixes.keySet()) {
				// a prefix name is valid if:
				// - it is prefixed (i.e. the unit name starts with it)
				// - it is longer than the existing largest prefix (since I am
				// looking for the longest valid prefix)
				// - the part after the prefix is a valid unit name
				// - the unit described that name is a linear unit (since only
				// linear units can have prefixes)
				if (unitName.startsWith(prefixName)
						&& prefixName.length() > longestLength) {
					final String rest = unitName.substring(prefixName.length());
					if (this.containsKey(rest)
							&& this.get(rest) instanceof LinearUnit) {
						longestPrefix = prefixName;
						longestLength = prefixName.length();
					}
				}
			}
			
			return longestPrefix != null;
		}
		
		/**
		 * {@inheritDoc}
		 * 
		 * <p>
		 * Because of ambiguities between prefixes (i.e. kilokilo = mega), this
		 * method only tests for prefixless units.
		 * </p>
		 */
		@Override
		public boolean containsValue(final Object value) {
			return this.units.containsValue(value);
		}
		
		@Override
		public Set<Entry<String, Unit>> entrySet() {
			if (this.entrySet == null) {
				this.entrySet = new PrefixedUnitEntrySet(this);
			}
			return this.entrySet;
		}
		
		@Override
		public Unit get(final Object key) {
			// First, test if there is a unit with the key
			if (this.units.containsKey(key))
				return this.units.get(key);
			
			// Next, try to cast it to String
			if (!(key instanceof String))
				throw new IllegalArgumentException(
						"Attempted to obtain a unit using a non-string name.");
			final String unitName = (String) key;
			
			// Then, look for the longest prefix that is attached to a valid unit
			String longestPrefix = null;
			int longestLength = 0;
			
			for (final String prefixName : this.prefixes.keySet()) {
				// a prefix name is valid if:
				// - it is prefixed (i.e. the unit name starts with it)
				// - it is longer than the existing largest prefix (since I am
				// looking for the longest valid prefix)
				// - the part after the prefix is a valid unit name
				// - the unit described that name is a linear unit (since only
				// linear units can have prefixes)
				if (unitName.startsWith(prefixName)
						&& prefixName.length() > longestLength) {
					final String rest = unitName.substring(prefixName.length());
					if (this.containsKey(rest)
							&& this.get(rest) instanceof LinearUnit) {
						longestPrefix = prefixName;
						longestLength = prefixName.length();
					}
				}
			}
			
			// if none found, returns null
			if (longestPrefix == null)
				return null;
			else {
				// get necessary data
				final String rest = unitName.substring(longestLength);
				// this cast will not fail because I verified that it would work
				// before selecting this prefix
				final LinearUnit unit = (LinearUnit) this.get(rest);
				final UnitPrefix prefix = this.prefixes.get(longestPrefix);
				
				return unit.withPrefix(prefix);
			}
		}
		
		@Override
		public boolean isEmpty() {
			return this.units.isEmpty();
		}
		
		@Override
		public Set<String> keySet() {
			if (this.keySet == null) {
				this.keySet = new PrefixedUnitNameSet(this);
			}
			return this.keySet;
		}
		
		@Override
		public Unit merge(final String key, final Unit value,
				final BiFunction<? super Unit, ? super Unit, ? extends Unit> remappingFunction) {
			throw new UnsupportedOperationException(
					"Cannot merge into an immutable map");
		}
		
		@Override
		public Unit put(final String key, final Unit value) {
			throw new UnsupportedOperationException(
					"Cannot add entries to an immutable map");
		}
		
		@Override
		public void putAll(final Map<? extends String, ? extends Unit> m) {
			throw new UnsupportedOperationException(
					"Cannot add entries to an immutable map");
		}
		
		@Override
		public Unit putIfAbsent(final String key, final Unit value) {
			throw new UnsupportedOperationException(
					"Cannot add entries to an immutable map");
		}
		
		@Override
		public Unit remove(final Object key) {
			throw new UnsupportedOperationException(
					"Cannot remove entries from an immutable map");
		}
		
		@Override
		public boolean remove(final Object key, final Object value) {
			throw new UnsupportedOperationException(
					"Cannot remove entries from an immutable map");
		}
		
		@Override
		public Unit replace(final String key, final Unit value) {
			throw new UnsupportedOperationException(
					"Cannot replace entries in an immutable map");
		}
		
		@Override
		public boolean replace(final String key, final Unit oldValue,
				final Unit newValue) {
			throw new UnsupportedOperationException(
					"Cannot replace entries in an immutable map");
		}
		
		@Override
		public void replaceAll(
				final BiFunction<? super String, ? super Unit, ? extends Unit> function) {
			throw new UnsupportedOperationException(
					"Cannot replace entries in an immutable map");
		}
		
		@Override
		public int size() {
			if (this.units.isEmpty())
				return 0;
			else {
				if (this.prefixes.isEmpty())
					return this.units.size();
				else
					// infinite set
					return Integer.MAX_VALUE;
			}
		}
		
		@Override
		public String toString() {
			if (this.units.isEmpty() || this.prefixes.isEmpty())
				return super.toString();
			else
				return String.format(
						"Infinite map of name-unit entries created from units %s and prefixes %s",
						this.units, this.prefixes);
		}
		
		/**
		 * {@inheritDoc}
		 * 
		 * <p>
		 * Because of ambiguities between prefixes (i.e. kilokilo = mega), this
		 * method ignores prefixes.
		 * </p>
		 */
		@Override
		public Collection<Unit> values() {
			if (this.values == null) {
				this.values = Collections
						.unmodifiableCollection(this.units.values());
			}
			return this.values;
		}
	}
	
	/**
	 * Replacements done to *all* expression types
	 */
	private static final Map<Pattern, String> EXPRESSION_REPLACEMENTS = new HashMap<>();
	
	// add data to expression replacements
	static {
		// add spaces around operators
		for (final String operator : Arrays.asList("\\*", "/", "\\^")) {
			EXPRESSION_REPLACEMENTS.put(Pattern.compile(operator),
					" " + operator + " ");
		}
		
		// replace multiple spaces with a single space
		EXPRESSION_REPLACEMENTS.put(Pattern.compile(" +"), " ");
		// place brackets around any expression of the form "number unit", with or
		// without the space
		EXPRESSION_REPLACEMENTS.put(Pattern.compile("((?:-?[1-9]\\d*|0)" // integer
				+ "(?:\\.\\d+(?:[eE]\\d+))?)" // optional decimal point with numbers
														// after it
				+ "\\s*" // optional space(s)
				+ "([a-zA-Z]+(?:\\^\\d+)?" // any string of letters
				+ "(?:\\s+[a-zA-Z]+(?:\\^\\d+)?))" // optional other letters
				+ "(?!-?\\d)" // no number directly afterwards (avoids matching
									// "1e3")
		), "\\($1 $2\\)");
	}
	
	/**
	 * A regular expression that separates names and expressions in unit files.
	 */
	private static final Pattern NAME_EXPRESSION = Pattern
			.compile("(\\S+)\\s+(\\S.*)");
	
	/**
	 * Like normal string comparisons, but shorter strings are always less than
	 * longer strings.
	 */
	private static final Comparator<String> lengthFirstComparator = Comparator
			.comparingInt(String::length).thenComparing(Comparator.naturalOrder());
	
	/**
	 * The exponent operator
	 * 
	 * @param base         base of exponentiation
	 * @param exponentUnit exponent
	 * @return result
	 * @since 2019-04-10
	 * @since v0.2.0
	 */
	private static final LinearUnit exponentiateUnits(final LinearUnit base,
			final LinearUnit exponentUnit) {
		// exponent function - first check if o2 is a number,
		if (exponentUnit.getBase().equals(Metric.ONE.getBase())) {
			// then check if it is an integer,
			final double exponent = exponentUnit.getConversionFactor();
			if (DecimalComparison.equals(exponent % 1, 0))
				// then exponentiate
				return base.toExponent((int) (exponent + 0.5));
			else
				// not an integer
				throw new UnsupportedOperationException(
						"Decimal exponents are currently not supported.");
		} else
			// not a number
			throw new IllegalArgumentException("Exponents must be numbers.");
	}
	
	/**
	 * The exponent operator
	 * 
	 * @param base         base of exponentiation
	 * @param exponentUnit exponent
	 * @return result
	 * @since 2020-08-04
	 */
	private static final LinearUnitValue exponentiateUnitValues(
			final LinearUnitValue base, final LinearUnitValue exponentValue) {
		// exponent function - first check if o2 is a number,
		if (exponentValue.canConvertTo(Metric.ONE)) {
			// then check if it is an integer,
			final double exponent = exponentValue.getValueExact();
			if (DecimalComparison.equals(exponent % 1, 0))
				// then exponentiate
				return base.toExponent((int) (exponent + 0.5));
			else
				// not an integer
				throw new UnsupportedOperationException(
						"Decimal exponents are currently not supported.");
		} else
			// not a number
			throw new IllegalArgumentException("Exponents must be numbers.");
	}
	
	/**
	 * @return true if entry represents a removable duplicate entry of unitMap.
	 * @since 2021-05-22
	 */
	private static boolean isRemovableDuplicate(Map<String, Unit> unitMap,
			Entry<String, Unit> entry) {
		for (final Entry<String, Unit> e : unitMap.entrySet()) {
			final String name = e.getKey();
			final Unit value = e.getValue();
			if (lengthFirstComparator.compare(entry.getKey(), name) < 0
					&& Objects.equals(unitMap.get(entry.getKey()), value))
				return true;
		}
		return false;
	}
	
	/**
	 * The units in this system, excluding prefixes.
	 * 
	 * @since 2019-01-07
	 * @since v0.1.0
	 */
	private final Map<String, Unit> prefixlessUnits;
	
	/**
	 * The unit prefixes in this system.
	 * 
	 * @since 2019-01-14
	 * @since v0.1.0
	 */
	private final Map<String, UnitPrefix> prefixes;
	
	/**
	 * The dimensions in this system.
	 * 
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	private final Map<String, ObjectProduct<BaseDimension>> dimensions;
	
	/**
	 * A map mapping strings to units (including prefixes)
	 * 
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	private final Map<String, Unit> units;
	
	/**
	 * The rule that specifies when prefix repetition is allowed. It takes in one
	 * argument: a list of the prefixes being applied to the unit
	 * <p>
	 * The prefixes are inputted in <em>application order</em>. This means that
	 * testing whether "kilomegagigametre" is a valid unit is equivalent to
	 * running the following code (assuming all variables are defined correctly):
	 * <br>
	 * {@code prefixRepetitionRule.test(Arrays.asList(giga, mega, kilo))}
	 */
	private Predicate<List<UnitPrefix>> prefixRepetitionRule;
	
	/**
	 * A parser that can parse unit expressions.
	 * 
	 * @since 2019-03-22
	 * @since v0.2.0
	 */
	private final ExpressionParser<LinearUnit> unitExpressionParser = new ExpressionParser.Builder<>(
			this::getLinearUnit).addBinaryOperator("+", (o1, o2) -> o1.plus(o2), 0)
					.addBinaryOperator("-", (o1, o2) -> o1.minus(o2), 0)
					.addBinaryOperator("*", (o1, o2) -> o1.times(o2), 1)
					.addSpaceFunction("*")
					.addBinaryOperator("/", (o1, o2) -> o1.dividedBy(o2), 1)
					.addBinaryOperator("^", UnitDatabase::exponentiateUnits, 2)
					.build();
	
	/**
	 * A parser that can parse unit value expressions.
	 * 
	 * @since 2020-08-04
	 */
	private final ExpressionParser<LinearUnitValue> unitValueExpressionParser = new ExpressionParser.Builder<>(
			this::getLinearUnitValue)
					.addBinaryOperator("+", (o1, o2) -> o1.plus(o2), 0)
					.addBinaryOperator("-", (o1, o2) -> o1.minus(o2), 0)
					.addBinaryOperator("*", (o1, o2) -> o1.times(o2), 1)
					.addSpaceFunction("*")
					.addBinaryOperator("/", (o1, o2) -> o1.dividedBy(o2), 1)
					.addBinaryOperator("^", UnitDatabase::exponentiateUnitValues, 2)
					.build();
	
	/**
	 * A parser that can parse unit prefix expressions
	 * 
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	private final ExpressionParser<UnitPrefix> prefixExpressionParser = new ExpressionParser.Builder<>(
			this::getPrefix).addBinaryOperator("*", (o1, o2) -> o1.times(o2), 0)
					.addSpaceFunction("*")
					.addBinaryOperator("/", (o1, o2) -> o1.dividedBy(o2), 0)
					.addBinaryOperator("^",
							(o1, o2) -> o1.toExponent(o2.getMultiplier()), 1)
					.build();
	
	/**
	 * A parser that can parse unit dimension expressions.
	 * 
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	private final ExpressionParser<ObjectProduct<BaseDimension>> unitDimensionParser = new ExpressionParser.Builder<>(
			this::getDimension).addBinaryOperator("*", (o1, o2) -> o1.times(o2), 0)
					.addSpaceFunction("*")
					.addBinaryOperator("/", (o1, o2) -> o1.dividedBy(o2), 0).build();
	
	/**
	 * Creates the {@code UnitsDatabase}.
	 * 
	 * @since 2019-01-10
	 * @since v0.1.0
	 */
	public UnitDatabase() {
		this(prefixes -> true);
	}
	
	/**
	 * Creates the {@code UnitsDatabase}
	 * 
	 * @param prefixRepetitionRule the rule that determines when prefix
	 *                             repetition is allowed
	 * @since 2020-08-26
	 */
	public UnitDatabase(Predicate<List<UnitPrefix>> prefixRepetitionRule) {
		this.prefixlessUnits = new HashMap<>();
		this.prefixes = new HashMap<>();
		this.dimensions = new HashMap<>();
		this.prefixRepetitionRule = prefixRepetitionRule;
		this.units = ConditionalExistenceCollections.conditionalExistenceMap(
				new PrefixedUnitMap(this.prefixlessUnits, this.prefixes),
				entry -> this.prefixRepetitionRule
						.test(this.getPrefixesFromName(entry.getKey())));
	}
	
	/**
	 * Adds a unit dimension to the database.
	 * 
	 * @param name      dimension's name
	 * @param dimension dimension to add
	 * @throws NullPointerException if name or dimension is null
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	public void addDimension(final String name,
			final ObjectProduct<BaseDimension> dimension) {
		this.dimensions.put(
				Objects.requireNonNull(name, "name must not be null."),
				Objects.requireNonNull(dimension, "dimension must not be null."));
	}
	
	/**
	 * Adds to the list from a line in a unit dimension file.
	 * 
	 * @param line        line to look at
	 * @param lineCounter number of line, for error messages
	 * @since 2019-04-10
	 * @since v0.2.0
	 */
	private void addDimensionFromLine(final String line,
			final long lineCounter) {
		// ignore lines that start with a # sign - they're comments
		if (line.isEmpty())
			return;
		if (line.contains("#")) {
			this.addDimensionFromLine(line.substring(0, line.indexOf("#")),
					lineCounter);
			return;
		}
		
		// divide line into name and expression
		final Matcher lineMatcher = NAME_EXPRESSION.matcher(line);
		if (!lineMatcher.matches())
			throw new IllegalArgumentException(String.format(
					"Error at line %d: Lines of a dimension file must consist of a dimension name, then spaces or tabs, then a dimension expression.",
					lineCounter));
		final String name = lineMatcher.group(1);
		final String expression = lineMatcher.group(2);
		
		if (name.endsWith(" ")) {
			System.err.printf("Warning - line %d's dimension name ends in a space",
					lineCounter);
		}
		
		// if expression is "!", search for an existing dimension
		// if no unit found, throw an error
		if (expression.equals("!")) {
			if (!this.containsDimensionName(name))
				throw new IllegalArgumentException(String.format(
						"! used but no dimension found (line %d).", lineCounter));
		} else {
			// it's a unit, get the unit
			final ObjectProduct<BaseDimension> dimension;
			try {
				dimension = this.getDimensionFromExpression(expression);
			} catch (final IllegalArgumentException e) {
				System.err.printf("Parsing error on line %d:%n", lineCounter);
				throw e;
			}
			
			this.addDimension(name, dimension);
		}
	}
	
	/**
	 * Adds a unit prefix to the database.
	 * 
	 * @param name   prefix's name
	 * @param prefix prefix to add
	 * @throws NullPointerException if name or prefix is null
	 * @since 2019-01-14
	 * @since v0.1.0
	 */
	public void addPrefix(final String name, final UnitPrefix prefix) {
		this.prefixes.put(Objects.requireNonNull(name, "name must not be null."),
				Objects.requireNonNull(prefix, "prefix must not be null."));
	}
	
	/**
	 * Adds a unit to the database.
	 * 
	 * @param name unit's name
	 * @param unit unit to add
	 * @throws NullPointerException if unit is null
	 * @since 2019-01-10
	 * @since v0.1.0
	 */
	public void addUnit(final String name, final Unit unit) {
		this.prefixlessUnits.put(
				Objects.requireNonNull(name, "name must not be null."),
				Objects.requireNonNull(unit, "unit must not be null."));
	}
	
	/**
	 * Adds to the list from a line in a unit file.
	 * 
	 * @param line        line to look at
	 * @param lineCounter number of line, for error messages
	 * @since 2019-04-10
	 * @since v0.2.0
	 */
	private void addUnitOrPrefixFromLine(final String line,
			final long lineCounter) {
		// ignore lines that start with a # sign - they're comments
		if (line.isEmpty())
			return;
		if (line.contains("#")) {
			this.addUnitOrPrefixFromLine(line.substring(0, line.indexOf("#")),
					lineCounter);
			return;
		}
		
		// divide line into name and expression
		final Matcher lineMatcher = NAME_EXPRESSION.matcher(line);
		if (!lineMatcher.matches())
			throw new IllegalArgumentException(String.format(
					"Error at line %d: Lines of a unit file must consist of a unit name, then spaces or tabs, then a unit expression.",
					lineCounter));
		final String name = lineMatcher.group(1);
		
		final String expression = lineMatcher.group(2);
		
		// this code should never occur
		// if (name.endsWith(" ")) {
		// System.err.printf("Warning - line %d's unit name ends in a space",
		// lineCounter);
		// }
		
		// if expression is "!", search for an existing unit
		// if no unit found, throw an error
		if (expression.equals("!")) {
			if (!this.containsUnitName(name))
				throw new IllegalArgumentException(String
						.format("! used but no unit found (line %d).", lineCounter));
		} else {
			if (name.endsWith("-")) {
				final UnitPrefix prefix;
				try {
					prefix = this.getPrefixFromExpression(expression);
				} catch (final IllegalArgumentException e) {
					System.err.printf("Parsing error on line %d:%n", lineCounter);
					throw e;
				}
				this.addPrefix(name.substring(0, name.length() - 1), prefix);
			} else {
				// it's a unit, get the unit
				final Unit unit;
				try {
					unit = this.getUnitFromExpression(expression);
				} catch (final IllegalArgumentException e) {
					System.err.printf("Parsing error on line %d:%n", lineCounter);
					throw e;
				}
				
				this.addUnit(name, unit);
			}
		}
	}
	
	/**
	 * Tests if the database has a unit dimension with this name.
	 * 
	 * @param name name to test
	 * @return if database contains name
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	public boolean containsDimensionName(final String name) {
		return this.dimensions.containsKey(name);
	}
	
	/**
	 * Tests if the database has a unit prefix with this name.
	 * 
	 * @param name name to test
	 * @return if database contains name
	 * @since 2019-01-13
	 * @since v0.1.0
	 */
	public boolean containsPrefixName(final String name) {
		return this.prefixes.containsKey(name);
	}
	
	/**
	 * Tests if the database has a unit with this name, taking prefixes into
	 * consideration
	 * 
	 * @param name name to test
	 * @return if database contains name
	 * @since 2019-01-13
	 * @since v0.1.0
	 */
	public boolean containsUnitName(final String name) {
		return this.units.containsKey(name);
	}
	
	/**
	 * @return a map mapping dimension names to dimensions
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	public Map<String, ObjectProduct<BaseDimension>> dimensionMap() {
		return Collections.unmodifiableMap(this.dimensions);
	}
	
	/**
	 * Evaluates a unit expression, following the same rules as
	 * {@link #getUnitFromExpression}.
	 * 
	 * @param expression expression to parse
	 * @return {@code LinearUnitValue} representing value of expression
	 * @since 2020-08-04
	 */
	public LinearUnitValue evaluateUnitExpression(final String expression) {
		Objects.requireNonNull(expression, "expression must not be null.");
		
		// attempt to get a unit as an alias, or a number with precision first
		if (this.containsUnitName(expression))
			return this.getLinearUnitValue(expression);
		
		// force operators to have spaces
		String modifiedExpression = expression;
		modifiedExpression = modifiedExpression.replaceAll("\\+", " \\+ ");
		modifiedExpression = modifiedExpression.replaceAll("-", " - ");
		
		// format expression
		for (final Entry<Pattern, String> replacement : EXPRESSION_REPLACEMENTS
				.entrySet()) {
			modifiedExpression = replacement.getKey().matcher(modifiedExpression)
					.replaceAll(replacement.getValue());
		}
		
		// the previous operation breaks negative numbers, fix them!
		// (i.e. -2 becomes - 2)
		// FIXME the previous operaton also breaks stuff like "1e-5"
		for (int i = 0; i < modifiedExpression.length(); i++) {
			if (modifiedExpression.charAt(i) == '-'
					&& (i < 2 || Arrays.asList('+', '-', '*', '/', '^')
							.contains(modifiedExpression.charAt(i - 2)))) {
				// found a broken negative number
				modifiedExpression = modifiedExpression.substring(0, i + 1)
						+ modifiedExpression.substring(i + 2);
			}
		}
		
		return this.unitValueExpressionParser.parseExpression(modifiedExpression);
	}
	
	/**
	 * Gets a unit dimension from the database using its name.
	 * 
	 * <p>
	 * This method accepts exponents, like "L^3"
	 * </p>
	 * 
	 * @param name dimension's name
	 * @return dimension
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	public ObjectProduct<BaseDimension> getDimension(final String name) {
		Objects.requireNonNull(name, "name must not be null.");
		if (name.contains("^")) {
			final String[] baseAndExponent = name.split("\\^");
			
			final ObjectProduct<BaseDimension> base = this
					.getDimension(baseAndExponent[0]);
			
			final int exponent;
			try {
				exponent = Integer
						.parseInt(baseAndExponent[baseAndExponent.length - 1]);
			} catch (final NumberFormatException e2) {
				throw new IllegalArgumentException("Exponent must be an integer.");
			}
			
			return base.toExponent(exponent);
		}
		return this.dimensions.get(name);
	}
	
	/**
	 * Uses the database's data to parse an expression into a unit dimension
	 * <p>
	 * The expression is a series of any of the following:
	 * <ul>
	 * <li>The name of a unit dimension, which multiplies or divides the result
	 * based on preceding operators</li>
	 * <li>The operators '*' and '/', which multiply and divide (note that just
	 * putting two unit dimensions next to each other is equivalent to
	 * multiplication)</li>
	 * <li>The operator '^' which exponentiates. Exponents must be integers.</li>
	 * </ul>
	 * 
	 * @param expression expression to parse
	 * @throws IllegalArgumentException if the expression cannot be parsed
	 * @throws NullPointerException     if expression is null
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	public ObjectProduct<BaseDimension> getDimensionFromExpression(
			final String expression) {
		Objects.requireNonNull(expression, "expression must not be null.");
		
		// attempt to get a dimension as an alias first
		if (this.containsDimensionName(expression))
			return this.getDimension(expression);
		
		// force operators to have spaces
		String modifiedExpression = expression;
		
		// format expression
		for (final Entry<Pattern, String> replacement : EXPRESSION_REPLACEMENTS
				.entrySet()) {
			modifiedExpression = replacement.getKey().matcher(modifiedExpression)
					.replaceAll(replacement.getValue());
		}
		modifiedExpression = modifiedExpression.replaceAll(" *\\^ *", "\\^");
		
		return this.unitDimensionParser.parseExpression(modifiedExpression);
	}
	
	/**
	 * Gets a unit. If it is linear, cast it to a LinearUnit and return it.
	 * Otherwise, throw an {@code IllegalArgumentException}.
	 * 
	 * @param name unit's name
	 * @return unit
	 * @since 2019-03-22
	 * @since v0.2.0
	 */
	private LinearUnit getLinearUnit(final String name) {
		// see if I am using a function-unit like tempC(100)
		Objects.requireNonNull(name, "name may not be null");
		if (name.contains("(") && name.contains(")")) {
			// break it into function name and value
			final List<String> parts = Arrays.asList(name.split("\\("));
			if (parts.size() != 2)
				throw new IllegalArgumentException(
						"Format nonlinear units like: unit(value).");
			
			// solve the function
			final Unit unit = this.getUnit(parts.get(0));
			final double value = Double.parseDouble(
					parts.get(1).substring(0, parts.get(1).length() - 1));
			return LinearUnit.fromUnitValue(unit, value);
		} else {
			// get a linear unit
			final Unit unit = this.getUnit(name);
			
			if (unit instanceof LinearUnit)
				return (LinearUnit) unit;
			else
				throw new IllegalArgumentException(
						String.format("%s is not a linear unit.", name));
		}
	}
	
	/**
	 * Gets a {@code LinearUnitValue} from a unit name. Nonlinear units will be
	 * converted to their base units.
	 * 
	 * @param name name of unit
	 * @return {@code LinearUnitValue} instance
	 * @since 2020-08-04
	 */
	private LinearUnitValue getLinearUnitValue(final String name) {
		try {
			// try to parse it as a number - otherwise it is not a number!
			final BigDecimal number = new BigDecimal(name);
			
			final double uncertainty = Math.pow(10, -number.scale());
			return LinearUnitValue.of(Metric.ONE,
					UncertainDouble.of(number.doubleValue(), uncertainty));
		} catch (final NumberFormatException e) {
			return LinearUnitValue.getExact(this.getLinearUnit(name), 1);
		}
	}
	
	/**
	 * Gets a unit prefix from the database from its name
	 * 
	 * @param name prefix's name
	 * @return prefix
	 * @since 2019-01-10
	 * @since v0.1.0
	 */
	public UnitPrefix getPrefix(final String name) {
		try {
			return UnitPrefix.valueOf(Double.parseDouble(name));
		} catch (final NumberFormatException e) {
			return this.prefixes.get(name);
		}
	}
	
	/**
	 * Gets all of the prefixes that are on a unit name, in application order.
	 * 
	 * @param unitName name of unit
	 * @return prefixes
	 * @since 2020-08-26
	 */
	List<UnitPrefix> getPrefixesFromName(final String unitName) {
		final List<UnitPrefix> prefixes = new ArrayList<>();
		String name = unitName;
		
		while (!this.prefixlessUnits.containsKey(name)) {
			// find the longest prefix
			String longestPrefixName = null;
			int longestLength = name.length();
			
			while (longestPrefixName == null) {
				longestLength--;
				if (longestLength <= 0)
					throw new AssertionError(
							"No prefix found in " + name + ", but it is not a unit!");
				if (this.prefixes.containsKey(name.substring(0, longestLength))) {
					longestPrefixName = name.substring(0, longestLength);
				}
			}
			
			// longest prefix found!
			final UnitPrefix prefix = this.getPrefix(longestPrefixName);
			prefixes.add(0, prefix);
			name = name.substring(longestLength);
		}
		return prefixes;
	}
	
	/**
	 * Gets a unit prefix from a prefix expression
	 * <p>
	 * Currently, prefix expressions are much simpler than unit expressions: They
	 * are either a number or the name of another prefix
	 * </p>
	 * 
	 * @param expression expression to input
	 * @return prefix
	 * @throws IllegalArgumentException if expression cannot be parsed
	 * @throws NullPointerException     if any argument is null
	 * @since 2019-01-14
	 * @since v0.1.0
	 */
	public UnitPrefix getPrefixFromExpression(final String expression) {
		Objects.requireNonNull(expression, "expression must not be null.");
		
		// attempt to get a unit as an alias first
		if (this.containsUnitName(expression))
			return this.getPrefix(expression);
		
		// force operators to have spaces
		String modifiedExpression = expression;
		
		// format expression
		for (final Entry<Pattern, String> replacement : EXPRESSION_REPLACEMENTS
				.entrySet()) {
			modifiedExpression = replacement.getKey().matcher(modifiedExpression)
					.replaceAll(replacement.getValue());
		}
		
		return this.prefixExpressionParser.parseExpression(modifiedExpression);
	}
	
	/**
	 * @return the prefixRepetitionRule
	 * @since 2020-08-26
	 */
	public final Predicate<List<UnitPrefix>> getPrefixRepetitionRule() {
		return this.prefixRepetitionRule;
	}
	
	/**
	 * Gets a unit from the database from its name, looking for prefixes.
	 * 
	 * @param name unit's name
	 * @return unit
	 * @since 2019-01-10
	 * @since v0.1.0
	 */
	public Unit getUnit(final String name) {
		try {
			final double value = Double.parseDouble(name);
			return Metric.ONE.times(value);
		} catch (final NumberFormatException e) {
			final Unit unit = this.units.get(name);
			if (unit == null)
				throw new NoSuchElementException("No unit " + name);
			else if (unit.getPrimaryName().isEmpty())
				return unit.withName(NameSymbol.ofName(name));
			else if (!unit.getPrimaryName().get().equals(name)) {
				final Set<String> otherNames = new HashSet<>(unit.getOtherNames());
				otherNames.add(unit.getPrimaryName().get());
				return unit.withName(NameSymbol.ofNullable(name,
						unit.getSymbol().orElse(null), otherNames));
			} else if (!unit.getOtherNames().contains(name)) {
				final Set<String> otherNames = new HashSet<>(unit.getOtherNames());
				otherNames.add(name);
				return unit.withName(
						NameSymbol.ofNullable(unit.getPrimaryName().orElse(null),
								unit.getSymbol().orElse(null), otherNames));
			} else
				return unit;
		}
		
	}
	
	/**
	 * Uses the database's unit data to parse an expression into a unit
	 * <p>
	 * The expression is a series of any of the following:
	 * <ul>
	 * <li>The name of a unit, which multiplies or divides the result based on
	 * preceding operators</li>
	 * <li>The operators '*' and '/', which multiply and divide (note that just
	 * putting two units or values next to each other is equivalent to
	 * multiplication)</li>
	 * <li>The operator '^' which exponentiates. Exponents must be integers.</li>
	 * <li>A number which is multiplied or divided</li>
	 * </ul>
	 * This method only works with linear units.
	 * 
	 * @param expression expression to parse
	 * @throws IllegalArgumentException if the expression cannot be parsed
	 * @throws NullPointerException     if expression is null
	 * @since 2019-01-07
	 * @since v0.1.0
	 */
	public Unit getUnitFromExpression(final String expression) {
		Objects.requireNonNull(expression, "expression must not be null.");
		
		// attempt to get a unit as an alias first
		if (this.containsUnitName(expression))
			return this.getUnit(expression);
		
		// force operators to have spaces
		String modifiedExpression = expression;
		modifiedExpression = modifiedExpression.replaceAll("\\+", " \\+ ");
		modifiedExpression = modifiedExpression.replaceAll("-", " - ");
		
		// format expression
		for (final Entry<Pattern, String> replacement : EXPRESSION_REPLACEMENTS
				.entrySet()) {
			modifiedExpression = replacement.getKey().matcher(modifiedExpression)
					.replaceAll(replacement.getValue());
		}
		
		// the previous operation breaks negative numbers, fix them!
		// (i.e. -2 becomes - 2)
		for (int i = 0; i < modifiedExpression.length(); i++) {
			if (modifiedExpression.charAt(i) == '-'
					&& (i < 2 || Arrays.asList('+', '-', '*', '/', '^')
							.contains(modifiedExpression.charAt(i - 2)))) {
				// found a broken negative number
				modifiedExpression = modifiedExpression.substring(0, i + 1)
						+ modifiedExpression.substring(i + 2);
			}
		}
		
		return this.unitExpressionParser.parseExpression(modifiedExpression);
	}
	
	/**
	 * Adds all dimensions from a file, using data from the database to parse
	 * them.
	 * <p>
	 * Each line in the file should consist of a name and an expression (parsed
	 * by getDimensionFromExpression) separated by any number of tab characters.
	 * <p>
	 * <p>
	 * Allowed exceptions:
	 * <ul>
	 * <li>Anything after a '#' character is considered a comment and
	 * ignored.</li>
	 * <li>Blank lines are also ignored</li>
	 * <li>If an expression consists of a single exclamation point, instead of
	 * parsing it, this method will search the database for an existing unit. If
	 * no unit is found, an IllegalArgumentException is thrown. This is used to
	 * define initial units and ensure that the database contains them.</li>
	 * </ul>
	 * 
	 * @param file file to read
	 * @throws IllegalArgumentException if the file cannot be parsed, found or
	 *                                  read
	 * @throws NullPointerException     if file is null
	 * @since 2019-01-13
	 * @since v0.1.0
	 */
	public void loadDimensionFile(final Path file) {
		Objects.requireNonNull(file, "file must not be null.");
		try {
			long lineCounter = 0;
			for (final String line : Files.readAllLines(file)) {
				this.addDimensionFromLine(line, ++lineCounter);
			}
		} catch (final FileNotFoundException e) {
			throw new IllegalArgumentException("Could not find file " + file, e);
		} catch (final IOException e) {
			throw new IllegalArgumentException("Could not read file " + file, e);
		}
	}
	
	/**
	 * Adds all dimensions from a {@code InputStream}. Otherwise, works like
	 * {@link #loadDimensionFile}.
	 *
	 * @param stream stream to load from
	 * @since 2021-03-27
	 */
	public void loadDimensionsFromStream(final InputStream stream) {
		try (final Scanner scanner = new Scanner(stream)) {
			long lineCounter = 0;
			while (scanner.hasNextLine()) {
				this.addDimensionFromLine(scanner.nextLine(), ++lineCounter);
			}
		}
	}
	
	/**
	 * Adds all units from a file, using data from the database to parse them.
	 * <p>
	 * Each line in the file should consist of a name and an expression (parsed
	 * by getUnitFromExpression) separated by any number of tab characters.
	 * <p>
	 * <p>
	 * Allowed exceptions:
	 * <ul>
	 * <li>Anything after a '#' character is considered a comment and
	 * ignored.</li>
	 * <li>Blank lines are also ignored</li>
	 * <li>If an expression consists of a single exclamation point, instead of
	 * parsing it, this method will search the database for an existing unit. If
	 * no unit is found, an IllegalArgumentException is thrown. This is used to
	 * define initial units and ensure that the database contains them.</li>
	 * </ul>
	 * 
	 * @param file file to read
	 * @throws IllegalArgumentException if the file cannot be parsed, found or
	 *                                  read
	 * @throws NullPointerException     if file is null
	 * @since 2019-01-13
	 * @since v0.1.0
	 */
	public void loadUnitsFile(final Path file) {
		Objects.requireNonNull(file, "file must not be null.");
		try {
			long lineCounter = 0;
			for (final String line : Files.readAllLines(file)) {
				this.addUnitOrPrefixFromLine(line, ++lineCounter);
			}
		} catch (final FileNotFoundException e) {
			throw new IllegalArgumentException("Could not find file " + file, e);
		} catch (final IOException e) {
			throw new IllegalArgumentException("Could not read file " + file, e);
		}
	}
	
	/**
	 * Adds all units from a {@code InputStream}. Otherwise, works like
	 * {@link #loadUnitsFile}.
	 *
	 * @param stream stream to load from
	 * @since 2021-03-27
	 */
	public void loadUnitsFromStream(InputStream stream) {
		try (final Scanner scanner = new Scanner(stream)) {
			long lineCounter = 0;
			while (scanner.hasNextLine()) {
				this.addUnitOrPrefixFromLine(scanner.nextLine(), ++lineCounter);
			}
		}
	}
	
	/**
	 * @return a map mapping prefix names to prefixes
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	public Map<String, UnitPrefix> prefixMap() {
		return Collections.unmodifiableMap(this.prefixes);
	}
	
	/**
	 * @param prefixRepetitionRule the prefixRepetitionRule to set
	 * @since 2020-08-26
	 */
	public final void setPrefixRepetitionRule(
			Predicate<List<UnitPrefix>> prefixRepetitionRule) {
		this.prefixRepetitionRule = prefixRepetitionRule;
	}
	
	/**
	 * @return a string stating the number of units, prefixes and dimensions in
	 *         the database
	 */
	@Override
	public String toString() {
		return String.format(
				"Unit Database with %d units, %d unit prefixes and %d dimensions",
				this.prefixlessUnits.size(), this.prefixes.size(),
				this.dimensions.size());
	}
	
	/**
	 * Returns a map mapping unit names to units, including units with prefixes.
	 * <p>
	 * The returned map is infinite in size if there is at least one unit and at
	 * least one prefix. If it is infinite, some operations that only work with
	 * finite collections, like converting name/entry sets to arrays, will throw
	 * an {@code IllegalStateException}.
	 * </p>
	 * <p>
	 * Specifically, the operations that will throw an IllegalStateException if
	 * the map is infinite in size are:
	 * <ul>
	 * <li>{@code unitMap.entrySet().toArray()} (either overloading)</li>
	 * <li>{@code unitMap.keySet().toArray()} (either overloading)</li>
	 * </ul>
	 * </p>
	 * <p>
	 * Because of ambiguities between prefixes (i.e. kilokilo = mega), the map's
	 * {@link PrefixedUnitMap#containsValue containsValue} and
	 * {@link PrefixedUnitMap#values() values()} methods currently ignore
	 * prefixes.
	 * </p>
	 * 
	 * @return a map mapping unit names to units, including prefixed names
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	public Map<String, Unit> unitMap() {
		return this.units; // PrefixedUnitMap is immutable so I don't need to make
									// an unmodifiable map.
	}
	
	/**
	 * @param includeDuplicates if true, duplicate units will all exist in the
	 *                          map; if false, only one of each unit will exist,
	 *                          even if the names are different
	 * @return a map mapping unit names to units, ignoring prefixes
	 * @since 2019-04-13
	 * @since v0.2.0
	 */
	public Map<String, Unit> unitMapPrefixless(boolean includeDuplicates) {
		if (includeDuplicates)
			return Collections.unmodifiableMap(this.prefixlessUnits);
		else
			return Collections.unmodifiableMap(ConditionalExistenceCollections
					.conditionalExistenceMap(this.prefixlessUnits,
							entry -> !isRemovableDuplicate(this.prefixlessUnits,
									entry)));
	}
}