Merge branch 'new-name' into develop

6 files changed, 2186 insertions, 0 deletions

diff --git a/src/main/java/sevenUnits/math/ConditionalExistenceCollections.java b/src/main/java/sevenUnits/math/ConditionalExistenceCollections.java
new file mode 100644
index 0000000..5ce1bd7
--- /dev/null
+++ b/src/main/java/sevenUnits/math/ConditionalExistenceCollections.java
@@ -0,0 +1,468 @@
+/**
+ * Copyright (C) 2019 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.math;
+
+import java.util.AbstractCollection;
+import java.util.AbstractMap;
+import java.util.AbstractSet;
+import java.util.Collection;
+import java.util.Iterator;
+import java.util.Map;
+import java.util.Map.Entry;
+import java.util.NoSuchElementException;
+import java.util.Set;
+import java.util.function.Predicate;
+
+/**
+ * Elements in these wrapper collections only exist if they pass a condition.
+ * <p>
+ * All of the collections in this class are "views" of the provided collections.
+ * They are mutable if the provided collections are mutable, they allow null if
+ * the provided collections allow null, they will reflect changes in the
+ * provided collection, etc.
+ * <p>
+ * The modification operations will always run the corresponding operations,
+ * even if the conditional existence collection doesn't change. For example, if
+ * you have a set that ignores even numbers, add(2) will still add a 2 to the
+ * backing set (but the conditional existence set will say it doesn't exist).
+ * <p>
+ * The returned collections do <i>not</i> pass the hashCode and equals
+ * operations through to the backing collections, but rely on {@code Object}'s
+ * {@code equals} and {@code hashCode} methods. This is necessary to preserve
+ * the contracts of these operations in the case that the backing collections
+ * are sets or lists.
+ * <p>
+ * Other than that, <i>the only difference between the provided collections and
+ * the returned collections are that elements don't exist if they don't pass the
+ * provided condition</i>.
+ * 
+ * 
+ * @author Adrien Hopkins
+ * @since 2019-10-17
+ */
+// TODO add conditional existence Lists and Sorted/Navigable Sets/Maps
+public final class ConditionalExistenceCollections {
+	/**
+	 * Elements in this collection only exist if they meet a condition.
+	 * 
+	 * @author Adrien Hopkins
+	 * @since 2019-10-17
+	 * @param <E> type of element in collection
+	 */
+	static final class ConditionalExistenceCollection<E>
+			extends AbstractCollection<E> {
+		final Collection<E> collection;
+		final Predicate<E> existenceCondition;
+		
+		/**
+		 * Creates the {@code ConditionalExistenceCollection}.
+		 * 
+		 * @param collection
+		 * @param existenceCondition
+		 * @since 2019-10-17
+		 */
+		private ConditionalExistenceCollection(final Collection<E> collection,
+				final Predicate<E> existenceCondition) {
+			this.collection = collection;
+			this.existenceCondition = existenceCondition;
+		}
+		
+		@Override
+		public boolean add(final E e) {
+			return this.collection.add(e) && this.existenceCondition.test(e);
+		}
+		
+		@Override
+		public void clear() {
+			this.collection.clear();
+		}
+		
+		@Override
+		public boolean contains(final Object o) {
+			if (!this.collection.contains(o))
+				return false;
+				
+			// this collection can only contain instances of E
+			// since the object is in the collection, we know that it must be an
+			// instance of E
+			// therefore this cast will always work
+			@SuppressWarnings("unchecked")
+			final E e = (E) o;
+			
+			return this.existenceCondition.test(e);
+		}
+		
+		@Override
+		public Iterator<E> iterator() {
+			return conditionalExistenceIterator(this.collection.iterator(),
+					this.existenceCondition);
+		}
+		
+		@Override
+		public boolean remove(final Object o) {
+			// remove() must be first in the && statement, otherwise it may not
+			// execute
+			final boolean containedObject = this.contains(o);
+			return this.collection.remove(o) && containedObject;
+		}
+		
+		@Override
+		public int size() {
+			return (int) this.collection.stream().filter(this.existenceCondition)
+					.count();
+		}
+		
+		@Override
+		public Object[] toArray() {
+			// ensure the toArray operation is supported
+			this.collection.toArray();
+			
+			// if it works, do it for real
+			return super.toArray();
+		}
+		
+		@Override
+		public <T> T[] toArray(T[] a) {
+			// ensure the toArray operation is supported
+			this.collection.toArray();
+			
+			// if it works, do it for real
+			return super.toArray(a);
+		}
+	}
+	
+	/**
+	 * Elements in this wrapper iterator only exist if they pass a condition.
+	 * 
+	 * @author Adrien Hopkins
+	 * @since 2019-10-17
+	 * @param <E> type of elements in iterator
+	 */
+	static final class ConditionalExistenceIterator<E> implements Iterator<E> {
+		final Iterator<E> iterator;
+		final Predicate<E> existenceCondition;
+		E nextElement;
+		boolean hasNext;
+		
+		/**
+		 * Creates the {@code ConditionalExistenceIterator}.
+		 * 
+		 * @param iterator
+		 * @param condition
+		 * @since 2019-10-17
+		 */
+		private ConditionalExistenceIterator(final Iterator<E> iterator,
+				final Predicate<E> condition) {
+			this.iterator = iterator;
+			this.existenceCondition = condition;
+			this.getAndSetNextElement();
+		}
+		
+		/**
+		 * Gets the next element, and sets nextElement and hasNext accordingly.
+		 * 
+		 * @since 2019-10-17
+		 */
+		private void getAndSetNextElement() {
+			do {
+				if (!this.iterator.hasNext()) {
+					this.nextElement = null;
+					this.hasNext = false;
+					return;
+				}
+				this.nextElement = this.iterator.next();
+			} while (!this.existenceCondition.test(this.nextElement));
+			this.hasNext = true;
+		}
+		
+		@Override
+		public boolean hasNext() {
+			return this.hasNext;
+		}
+		
+		@Override
+		public E next() {
+			if (this.hasNext()) {
+				final E next = this.nextElement;
+				this.getAndSetNextElement();
+				return next;
+			} else
+				throw new NoSuchElementException();
+		}
+		
+		@Override
+		public void remove() {
+			this.iterator.remove();
+		}
+	}
+	
+	/**
+	 * Mappings in this map only exist if the entry passes some condition.
+	 * 
+	 * @author Adrien Hopkins
+	 * @since 2019-10-17
+	 * @param <K> key type
+	 * @param <V> value type
+	 */
+	static final class ConditionalExistenceMap<K, V> extends AbstractMap<K, V> {
+		Map<K, V> map;
+		Predicate<Entry<K, V>> entryExistenceCondition;
+		
+		/**
+		 * Creates the {@code ConditionalExistenceMap}.
+		 * 
+		 * @param map
+		 * @param entryExistenceCondition
+		 * @since 2019-10-17
+		 */
+		private ConditionalExistenceMap(final Map<K, V> map,
+				final Predicate<Entry<K, V>> entryExistenceCondition) {
+			this.map = map;
+			this.entryExistenceCondition = entryExistenceCondition;
+		}
+		
+		@Override
+		public boolean containsKey(final Object key) {
+			if (!this.map.containsKey(key))
+				return false;
+				
+			// only instances of K have mappings in the backing map
+			// since we know that key is a valid key, it must be an instance of K
+			@SuppressWarnings("unchecked")
+			final K keyAsK = (K) key;
+			
+			// get and test entry
+			final V value = this.map.get(key);
+			final Entry<K, V> entry = new SimpleEntry<>(keyAsK, value);
+			return this.entryExistenceCondition.test(entry);
+		}
+		
+		@Override
+		public Set<Entry<K, V>> entrySet() {
+			return conditionalExistenceSet(this.map.entrySet(),
+					this.entryExistenceCondition);
+		}
+		
+		@Override
+		public V get(final Object key) {
+			return this.containsKey(key) ? this.map.get(key) : null;
+		}
+		
+		private final Entry<K, V> getEntry(K key) {
+			return new Entry<>() {
+				@Override
+				public K getKey() {
+					return key;
+				}
+				
+				@Override
+				public V getValue() {
+					return ConditionalExistenceMap.this.map.get(key);
+				}
+				
+				@Override
+				public V setValue(V value) {
+					return ConditionalExistenceMap.this.map.put(key, value);
+				}
+			};
+		}
+		
+		@Override
+		public Set<K> keySet() {
+			return conditionalExistenceSet(super.keySet(),
+					k -> this.entryExistenceCondition.test(this.getEntry(k)));
+		}
+		
+		@Override
+		public V put(final K key, final V value) {
+			final V oldValue = this.map.put(key, value);
+			
+			// get and test entry
+			final Entry<K, V> entry = new SimpleEntry<>(key, oldValue);
+			return this.entryExistenceCondition.test(entry) ? oldValue : null;
+		}
+		
+		@Override
+		public V remove(final Object key) {
+			final V oldValue = this.map.remove(key);
+			return this.containsKey(key) ? oldValue : null;
+		}
+		
+		@Override
+		public Collection<V> values() {
+			// maybe change this to use ConditionalExistenceCollection
+			return super.values();
+		}
+	}
+	
+	/**
+	 * Elements in this set only exist if a certain condition is true.
+	 * 
+	 * @author Adrien Hopkins
+	 * @since 2019-10-17
+	 * @param <E> type of element in set
+	 */
+	static final class ConditionalExistenceSet<E> extends AbstractSet<E> {
+		private final Set<E> set;
+		private final Predicate<E> existenceCondition;
+		
+		/**
+		 * Creates the {@code ConditionalNonexistenceSet}.
+		 * 
+		 * @param set                set to use
+		 * @param existenceCondition condition where element exists
+		 * @since 2019-10-17
+		 */
+		private ConditionalExistenceSet(final Set<E> set,
+				final Predicate<E> existenceCondition) {
+			this.set = set;
+			this.existenceCondition = existenceCondition;
+		}
+		
+		/**
+		 * {@inheritDoc}
+		 * <p>
+		 * Note that this method returns {@code false} if {@code e} does not pass
+		 * the existence condition.
+		 */
+		@Override
+		public boolean add(final E e) {
+			return this.set.add(e) && this.existenceCondition.test(e);
+		}
+		
+		@Override
+		public void clear() {
+			this.set.clear();
+		}
+		
+		@Override
+		public boolean contains(final Object o) {
+			if (!this.set.contains(o))
+				return false;
+				
+			// this set can only contain instances of E
+			// since the object is in the set, we know that it must be an instance
+			// of E
+			// therefore this cast will always work
+			@SuppressWarnings("unchecked")
+			final E e = (E) o;
+			
+			return this.existenceCondition.test(e);
+		}
+		
+		@Override
+		public Iterator<E> iterator() {
+			return conditionalExistenceIterator(this.set.iterator(),
+					this.existenceCondition);
+		}
+		
+		@Override
+		public boolean remove(final Object o) {
+			// remove() must be first in the && statement, otherwise it may not
+			// execute
+			final boolean containedObject = this.contains(o);
+			return this.set.remove(o) && containedObject;
+		}
+		
+		@Override
+		public int size() {
+			return (int) this.set.stream().filter(this.existenceCondition).count();
+		}
+		
+		@Override
+		public Object[] toArray() {
+			// ensure the toArray operation is supported
+			this.set.toArray();
+			
+			// if it works, do it for real
+			return super.toArray();
+		}
+		
+		@Override
+		public <T> T[] toArray(T[] a) {
+			// ensure the toArray operation is supported
+			this.set.toArray();
+			
+			// if it works, do it for real
+			return super.toArray(a);
+		}
+	}
+	
+	/**
+	 * Elements in the returned wrapper collection are ignored if they don't pass
+	 * a condition.
+	 * 
+	 * @param <E>                type of elements in collection
+	 * @param collection         collection to wrap
+	 * @param existenceCondition elements only exist if this returns true
+	 * @return wrapper collection
+	 * @since 2019-10-17
+	 */
+	public static final <E> Collection<E> conditionalExistenceCollection(
+			final Collection<E> collection,
+			final Predicate<E> existenceCondition) {
+		return new ConditionalExistenceCollection<>(collection,
+				existenceCondition);
+	}
+	
+	/**
+	 * Elements in the returned wrapper iterator are ignored if they don't pass a
+	 * condition.
+	 * 
+	 * @param <E>                type of elements in iterator
+	 * @param iterator           iterator to wrap
+	 * @param existenceCondition elements only exist if this returns true
+	 * @return wrapper iterator
+	 * @since 2019-10-17
+	 */
+	public static final <E> Iterator<E> conditionalExistenceIterator(
+			final Iterator<E> iterator, final Predicate<E> existenceCondition) {
+		return new ConditionalExistenceIterator<>(iterator, existenceCondition);
+	}
+	
+	/**
+	 * Mappings in the returned wrapper map are ignored if the corresponding
+	 * entry doesn't pass a condition
+	 * 
+	 * @param <K>                     type of key in map
+	 * @param <V>                     type of value in map
+	 * @param map                     map to wrap
+	 * @param entryExistenceCondition mappings only exist if this returns true
+	 * @return wrapper map
+	 * @since 2019-10-17
+	 */
+	public static final <K, V> Map<K, V> conditionalExistenceMap(
+			final Map<K, V> map,
+			final Predicate<Entry<K, V>> entryExistenceCondition) {
+		return new ConditionalExistenceMap<>(map, entryExistenceCondition);
+	}
+	
+	/**
+	 * Elements in the returned wrapper set are ignored if they don't pass a
+	 * condition.
+	 * 
+	 * @param <E>                type of elements in set
+	 * @param set                set to wrap
+	 * @param existenceCondition elements only exist if this returns true
+	 * @return wrapper set
+	 * @since 2019-10-17
+	 */
+	public static final <E> Set<E> conditionalExistenceSet(final Set<E> set,
+			final Predicate<E> existenceCondition) {
+		return new ConditionalExistenceSet<>(set, existenceCondition);
+	}
+}
diff --git a/src/main/java/sevenUnits/math/DecimalComparison.java b/src/main/java/sevenUnits/math/DecimalComparison.java
new file mode 100644
index 0000000..24a9b2f
--- /dev/null
+++ b/src/main/java/sevenUnits/math/DecimalComparison.java
@@ -0,0 +1,256 @@
+/**
+ * Copyright (C) 2019 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.math;
+
+import java.math.BigDecimal;
+
+/**
+ * A class that contains methods to compare float and double values.
+ * 
+ * @author Adrien Hopkins
+ * @since 2019-03-18
+ * @since v0.2.0
+ */
+public final class DecimalComparison {
+	/**
+	 * The value used for double comparison. If two double values are within this
+	 * value multiplied by the larger value, they are considered equal.
+	 * 
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 */
+	public static final double DOUBLE_EPSILON = 1.0e-15;
+	
+	/**
+	 * The value used for float comparison. If two float values are within this
+	 * value multiplied by the larger value, they are considered equal.
+	 * 
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 */
+	public static final float FLOAT_EPSILON = 1.0e-6f;
+	
+	/**
+	 * Tests for equality of double values using {@link #DOUBLE_EPSILON}.
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon using
+	 * {@link #equals(double, double, double)} (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a first value to test
+	 * @param b second value to test
+	 * @return whether they are equal
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 * @see #hashCode(double)
+	 */
+	public static final boolean equals(final double a, final double b) {
+		return DecimalComparison.equals(a, b, DOUBLE_EPSILON);
+	}
+	
+	/**
+	 * Tests for double equality using a custom epsilon value.
+	 * 
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a       first value to test
+	 * @param b       second value to test
+	 * @param epsilon allowed difference
+	 * @return whether they are equal
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 */
+	public static final boolean equals(final double a, final double b,
+			final double epsilon) {
+		return Math.abs(a - b) <= epsilon * Math.max(Math.abs(a), Math.abs(b));
+	}
+	
+	/**
+	 * Tests for equality of float values using {@link #FLOAT_EPSILON}.
+	 * 
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon using {@link #equals(float, float, float)}
+	 * (this does not make a violation of transitivity impossible, it just
+	 * significantly reduces the chances of it happening)
+	 * <li>Use {@link BigDecimal} instead of {@code float} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a first value to test
+	 * @param b second value to test
+	 * @return whether they are equal
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 */
+	public static final boolean equals(final float a, final float b) {
+		return DecimalComparison.equals(a, b, FLOAT_EPSILON);
+	}
+	
+	/**
+	 * Tests for float equality using a custom epsilon value.
+	 * 
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code float} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a       first value to test
+	 * @param b       second value to test
+	 * @param epsilon allowed difference
+	 * @return whether they are equal
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 */
+	public static final boolean equals(final float a, final float b,
+			final float epsilon) {
+		return Math.abs(a - b) <= epsilon * Math.max(Math.abs(a), Math.abs(b));
+	}
+	
+	/**
+	 * Tests for equality of {@code UncertainDouble} values using
+	 * {@link #DOUBLE_EPSILON}.
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon using
+	 * {@link #equals(UncertainDouble, UncertainDouble, double)} (this does not
+	 * make a violation of transitivity impossible, it just significantly reduces
+	 * the chances of it happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a first value to test
+	 * @param b second value to test
+	 * @return whether they are equal
+	 * @since 2020-09-07
+	 * @see #hashCode(double)
+	 */
+	public static final boolean equals(final UncertainDouble a,
+			final UncertainDouble b) {
+		return DecimalComparison.equals(a.value(), b.value())
+				&& DecimalComparison.equals(a.uncertainty(), b.uncertainty());
+	}
+	
+	/**
+	 * Tests for {@code UncertainDouble} equality using a custom epsilon value.
+	 * 
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a       first value to test
+	 * @param b       second value to test
+	 * @param epsilon allowed difference
+	 * @return whether they are equal
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 */
+	public static final boolean equals(final UncertainDouble a,
+			final UncertainDouble b, final double epsilon) {
+		return DecimalComparison.equals(a.value(), b.value(), epsilon)
+				&& DecimalComparison.equals(a.uncertainty(), b.uncertainty(),
+						epsilon);
+	}
+	
+	/**
+	 * Takes the hash code of doubles. Values that are equal according to
+	 * {@link #equals(double, double)} will have the same hash code.
+	 * 
+	 * @param d double to hash
+	 * @return hash code of double
+	 * @since 2019-10-16
+	 */
+	public static final int hash(final double d) {
+		return Float.hashCode((float) d);
+	}
+	
+	// You may NOT get any DecimalComparison instances
+	private DecimalComparison() {
+		throw new AssertionError();
+	}
+	
+}
diff --git a/src/main/java/sevenUnits/math/ExpressionParser.java b/src/main/java/sevenUnits/math/ExpressionParser.java
new file mode 100644
index 0000000..5c8183b
--- /dev/null
+++ b/src/main/java/sevenUnits/math/ExpressionParser.java
@@ -0,0 +1,735 @@
+/**
+ * Copyright (C) 2019 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.math;
+
+import java.util.ArrayDeque;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.Deque;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.function.BinaryOperator;
+import java.util.function.Function;
+import java.util.function.UnaryOperator;
+
+/**
+ * An object that can parse expressions with unary or binary operators.
+ * 
+ * @author Adrien Hopkins
+ * @param <T> type of object that exists in parsed expressions
+ * @since 2019-03-14
+ * @since v0.2.0
+ */
+public final class ExpressionParser<T> {
+	/**
+	 * A builder that can create {@code ExpressionParser<T>} instances.
+	 * 
+	 * @author Adrien Hopkins
+	 * @param <T> type of object that exists in parsed expressions
+	 * @since 2019-03-17
+	 * @since v0.2.0
+	 */
+	public static final class Builder<T> {
+		/**
+		 * A function that obtains a parseable object from a string. For example,
+		 * an integer {@code ExpressionParser} would use
+		 * {@code Integer::parseInt}.
+		 * 
+		 * @since 2019-03-14
+		 * @since v0.2.0
+		 */
+		private final Function<String, ? extends T> objectObtainer;
+		
+		/**
+		 * The function of the space as an operator (like 3 x y)
+		 * 
+		 * @since 2019-03-22
+		 * @since v0.2.0
+		 */
+		private String spaceFunction = null;
+		
+		/**
+		 * A map mapping operator strings to operator functions, for unary
+		 * operators.
+		 * 
+		 * @since 2019-03-14
+		 * @since v0.2.0
+		 */
+		private final Map<String, PriorityUnaryOperator<T>> unaryOperators;
+		
+		/**
+		 * A map mapping operator strings to operator functions, for binary
+		 * operators.
+		 * 
+		 * @since 2019-03-14
+		 * @since v0.2.0
+		 */
+		private final Map<String, PriorityBinaryOperator<T>> binaryOperators;
+		
+		/**
+		 * Creates the {@code Builder}.
+		 * 
+		 * @param objectObtainer a function that can turn strings into objects of
+		 *                       the type handled by the parser.
+		 * @throws NullPointerException if {@code objectObtainer} is null
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		public Builder(final Function<String, ? extends T> objectObtainer) {
+			this.objectObtainer = Objects.requireNonNull(objectObtainer,
+					"objectObtainer must not be null.");
+			this.unaryOperators = new HashMap<>();
+			this.binaryOperators = new HashMap<>();
+		}
+		
+		/**
+		 * Adds a binary operator to the builder.
+		 * 
+		 * @param text     text used to reference the operator, like '+'
+		 * @param operator operator to add
+		 * @param priority operator's priority, which determines which operators
+		 *                 are applied first
+		 * @return this builder
+		 * @throws NullPointerException if {@code text} or {@code operator} is
+		 *                              null
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		public Builder<T> addBinaryOperator(final String text,
+				final BinaryOperator<T> operator, final int priority) {
+			Objects.requireNonNull(text, "text must not be null.");
+			Objects.requireNonNull(operator, "operator must not be null.");
+			
+			// Unfortunately, I cannot use a lambda because the
+			// PriorityBinaryOperator requires arguments.
+			final PriorityBinaryOperator<T> priorityOperator = new PriorityBinaryOperator<>(
+					priority) {
+				@Override
+				public T apply(final T t, final T u) {
+					return operator.apply(t, u);
+				}
+				
+			};
+			this.binaryOperators.put(text, priorityOperator);
+			return this;
+		}
+		
+		/**
+		 * Adds a function for spaces. You must use the text of an existing binary
+		 * operator.
+		 * 
+		 * @param operator text of operator to use
+		 * @return this builder
+		 * @since 2019-03-22
+		 * @since v0.2.0
+		 */
+		public Builder<T> addSpaceFunction(final String operator) {
+			Objects.requireNonNull(operator, "operator must not be null.");
+			
+			if (!this.binaryOperators.containsKey(operator))
+				throw new IllegalArgumentException(String
+						.format("Could not find binary operator '%s'", operator));
+			
+			this.spaceFunction = operator;
+			return this;
+		}
+		
+		/**
+		 * Adds a unary operator to the builder.
+		 * 
+		 * @param text     text used to reference the operator, like '-'
+		 * @param operator operator to add
+		 * @param priority operator's priority, which determines which operators
+		 *                 are applied first
+		 * @return this builder
+		 * @throws NullPointerException if {@code text} or {@code operator} is
+		 *                              null
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		public Builder<T> addUnaryOperator(final String text,
+				final UnaryOperator<T> operator, final int priority) {
+			Objects.requireNonNull(text, "text must not be null.");
+			Objects.requireNonNull(operator, "operator must not be null.");
+			
+			// Unfortunately, I cannot use a lambda because the
+			// PriorityUnaryOperator requires arguments.
+			final PriorityUnaryOperator<T> priorityOperator = new PriorityUnaryOperator<>(
+					priority) {
+				@Override
+				public T apply(final T t) {
+					return operator.apply(t);
+				}
+			};
+			this.unaryOperators.put(text, priorityOperator);
+			return this;
+		}
+		
+		/**
+		 * @return an {@code ExpressionParser<T>} instance with the properties
+		 *         given to this builder
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		public ExpressionParser<T> build() {
+			return new ExpressionParser<>(this.objectObtainer, this.unaryOperators,
+					this.binaryOperators, this.spaceFunction);
+		}
+	}
+	
+	/**
+	 * A binary operator with a priority field that determines which operators
+	 * apply first.
+	 * 
+	 * @author Adrien Hopkins
+	 * @param <T> type of operand and result
+	 * @since 2019-03-17
+	 * @since v0.2.0
+	 */
+	private static abstract class PriorityBinaryOperator<T>
+			implements BinaryOperator<T>, Comparable<PriorityBinaryOperator<T>> {
+		/**
+		 * The operator's priority. Higher-priority operators are applied before
+		 * lower-priority operators
+		 * 
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		private final int priority;
+		
+		/**
+		 * Creates the {@code PriorityBinaryOperator}.
+		 * 
+		 * @param priority operator's priority
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		public PriorityBinaryOperator(final int priority) {
+			this.priority = priority;
+		}
+		
+		/**
+		 * Compares this object to another by priority.
+		 * 
+		 * <p>
+		 * {@inheritDoc}
+		 * </p>
+		 * 
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		@Override
+		public int compareTo(final PriorityBinaryOperator<T> o) {
+			if (this.priority < o.priority)
+				return -1;
+			else if (this.priority > o.priority)
+				return 1;
+			else
+				return 0;
+		}
+		
+		/**
+		 * @return priority
+		 * @since 2019-03-22
+		 * @since v0.2.0
+		 */
+		public final int getPriority() {
+			return this.priority;
+		}
+	}
+	
+	/**
+	 * A unary operator with a priority field that determines which operators
+	 * apply first.
+	 * 
+	 * @author Adrien Hopkins
+	 * @param <T> type of operand and result
+	 * @since 2019-03-17
+	 * @since v0.2.0
+	 */
+	private static abstract class PriorityUnaryOperator<T>
+			implements UnaryOperator<T>, Comparable<PriorityUnaryOperator<T>> {
+		/**
+		 * The operator's priority. Higher-priority operators are applied before
+		 * lower-priority operators
+		 * 
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		private final int priority;
+		
+		/**
+		 * Creates the {@code PriorityUnaryOperator}.
+		 * 
+		 * @param priority operator's priority
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		public PriorityUnaryOperator(final int priority) {
+			this.priority = priority;
+		}
+		
+		/**
+		 * Compares this object to another by priority.
+		 * 
+		 * <p>
+		 * {@inheritDoc}
+		 * </p>
+		 * 
+		 * @since 2019-03-17
+		 * @since v0.2.0
+		 */
+		@Override
+		public int compareTo(final PriorityUnaryOperator<T> o) {
+			if (this.priority < o.priority)
+				return -1;
+			else if (this.priority > o.priority)
+				return 1;
+			else
+				return 0;
+		}
+		
+		/**
+		 * @return priority
+		 * @since 2019-03-22
+		 * @since v0.2.0
+		 */
+		public final int getPriority() {
+			return this.priority;
+		}
+	}
+	
+	/**
+	 * The types of tokens that are available.
+	 * 
+	 * @author Adrien Hopkins
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	private static enum TokenType {
+		OBJECT, UNARY_OPERATOR, BINARY_OPERATOR;
+	}
+	
+	/**
+	 * The opening bracket.
+	 * 
+	 * @since 2019-03-22
+	 * @since v0.2.0
+	 */
+	public static final char OPENING_BRACKET = '(';
+	
+	/**
+	 * The closing bracket.
+	 * 
+	 * @since 2019-03-22
+	 * @since v0.2.0
+	 */
+	public static final char CLOSING_BRACKET = ')';
+	
+	/**
+	 * Finds the other bracket in a pair of brackets, given the position of one.
+	 * 
+	 * @param string          string that contains brackets
+	 * @param bracketPosition position of first bracket
+	 * @return position of matching bracket
+	 * @throws NullPointerException if string is null
+	 * @since 2019-03-22
+	 * @since v0.2.0
+	 */
+	private static int findBracketPair(final String string,
+			final int bracketPosition) {
+		Objects.requireNonNull(string, "string must not be null.");
+		
+		final char openingBracket = string.charAt(bracketPosition);
+		
+		// figure out what closing bracket to look for
+		final char closingBracket;
+		switch (openingBracket) {
+		case '(':
+			closingBracket = ')';
+			break;
+		case '[':
+			closingBracket = ']';
+			break;
+		case '{':
+			closingBracket = '}';
+			break;
+		default:
+			throw new IllegalArgumentException(
+					String.format("Invalid bracket '%s'", openingBracket));
+		}
+		
+		// level of brackets. every opening bracket increments this; every closing
+		// bracket decrements it
+		int bracketLevel = 0;
+		
+		// iterate over the string to find the closing bracket
+		for (int currentPosition = bracketPosition; currentPosition < string
+				.length(); currentPosition++) {
+			final char currentCharacter = string.charAt(currentPosition);
+			
+			if (currentCharacter == openingBracket) {
+				bracketLevel++;
+			} else if (currentCharacter == closingBracket) {
+				bracketLevel--;
+				if (bracketLevel == 0)
+					return currentPosition;
+			}
+		}
+		
+		throw new IllegalArgumentException("No matching bracket found.");
+	}
+	
+	/**
+	 * A function that obtains a parseable object from a string. For example, an
+	 * integer {@code ExpressionParser} would use {@code Integer::parseInt}.
+	 * 
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	private final Function<String, ? extends T> objectObtainer;
+	
+	/**
+	 * A map mapping operator strings to operator functions, for unary operators.
+	 * 
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	private final Map<String, PriorityUnaryOperator<T>> unaryOperators;
+	
+	/**
+	 * A map mapping operator strings to operator functions, for binary
+	 * operators.
+	 * 
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	private final Map<String, PriorityBinaryOperator<T>> binaryOperators;
+	
+	/**
+	 * The operator for space, or null if spaces have no function.
+	 * 
+	 * @since 2019-03-22
+	 * @since v0.2.0
+	 */
+	private final String spaceOperator;
+	
+	/**
+	 * Creates the {@code ExpressionParser}.
+	 * 
+	 * @param objectObtainer  function to get objects from strings
+	 * @param unaryOperators  unary operators available to the parser
+	 * @param binaryOperators binary operators available to the parser
+	 * @param spaceOperator   operator used by spaces
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	private ExpressionParser(final Function<String, ? extends T> objectObtainer,
+			final Map<String, PriorityUnaryOperator<T>> unaryOperators,
+			final Map<String, PriorityBinaryOperator<T>> binaryOperators,
+			final String spaceOperator) {
+		this.objectObtainer = objectObtainer;
+		this.unaryOperators = unaryOperators;
+		this.binaryOperators = binaryOperators;
+		this.spaceOperator = spaceOperator;
+	}
+	
+	/**
+	 * Converts a given mathematical expression to reverse Polish notation
+	 * (operators after operands).
+	 * <p>
+	 * For example,<br>
+	 * {@code 2 * (3 + 4)}<br>
+	 * becomes<br>
+	 * {@code 2 3 4 + *}.
+	 * 
+	 * @param expression expression
+	 * @return expression in RPN
+	 * @since 2019-03-17
+	 * @since v0.2.0
+	 */
+	private String convertExpressionToReversePolish(final String expression) {
+		Objects.requireNonNull(expression, "expression must not be null.");
+		
+		final List<String> components = new ArrayList<>();
+		
+		// the part of the expression remaining to parse
+		String partialExpression = expression;
+		
+		// find and deal with brackets
+		while (partialExpression.indexOf(OPENING_BRACKET) != -1) {
+			final int openingBracketPosition = partialExpression
+					.indexOf(OPENING_BRACKET);
+			final int closingBracketPosition = findBracketPair(partialExpression,
+					openingBracketPosition);
+			
+			// check for function
+			if (openingBracketPosition > 0
+					&& partialExpression.charAt(openingBracketPosition - 1) != ' ') {
+				// function like sin(2) or tempF(32)
+				// find the position of the last space
+				int spacePosition = openingBracketPosition;
+				while (spacePosition >= 0
+						&& partialExpression.charAt(spacePosition) != ' ') {
+					spacePosition--;
+				}
+				// then split the function into pre-function and function, using the
+				// space position
+				components.addAll(Arrays.asList(partialExpression
+						.substring(0, spacePosition + 1).split(" ")));
+				components.add(partialExpression.substring(spacePosition + 1,
+						closingBracketPosition + 1));
+				partialExpression = partialExpression
+						.substring(closingBracketPosition + 1);
+			} else {
+				// normal brackets like (1 + 2) * (3 / 5)
+				components.addAll(Arrays.asList(partialExpression
+						.substring(0, openingBracketPosition).split(" ")));
+				components.add(this.convertExpressionToReversePolish(
+						partialExpression.substring(openingBracketPosition + 1,
+								closingBracketPosition)));
+				partialExpression = partialExpression
+						.substring(closingBracketPosition + 1);
+			}
+		}
+		
+		// add everything else
+		components.addAll(Arrays.asList(partialExpression.split(" ")));
+		
+		// remove empty entries
+		while (components.contains("")) {
+			components.remove("");
+		}
+		
+		// deal with space multiplication (x y)
+		if (this.spaceOperator != null) {
+			for (int i = 0; i < components.size() - 1; i++) {
+				if (this.getTokenType(components.get(i)) == TokenType.OBJECT && this
+						.getTokenType(components.get(i + 1)) == TokenType.OBJECT) {
+					components.add(++i, this.spaceOperator);
+				}
+			}
+		}
+		
+		// turn the expression into reverse Polish
+		while (true) {
+			final int highestPriorityOperatorPosition = this
+					.findHighestPriorityOperatorPosition(components);
+			if (highestPriorityOperatorPosition == -1) {
+				break;
+			}
+			
+			// swap components based on what kind of operator there is
+			// 1 + 2 becomes 2 1 +
+			// - 1 becomes 1 -
+			switch (this
+					.getTokenType(components.get(highestPriorityOperatorPosition))) {
+			case UNARY_OPERATOR:
+				final String unaryOperator = components
+						.remove(highestPriorityOperatorPosition);
+				final String operand = components
+						.remove(highestPriorityOperatorPosition);
+				components.add(highestPriorityOperatorPosition,
+						operand + " " + unaryOperator);
+				break;
+			case BINARY_OPERATOR:
+				final String binaryOperator = components
+						.remove(highestPriorityOperatorPosition);
+				final String operand1 = components
+						.remove(highestPriorityOperatorPosition - 1);
+				final String operand2 = components
+						.remove(highestPriorityOperatorPosition - 1);
+				components.add(highestPriorityOperatorPosition - 1,
+						operand2 + " " + operand1 + " " + binaryOperator);
+				break;
+			default:
+				throw new AssertionError("Expected operator, found non-operator.");
+			}
+		}
+		
+		// join all of the components together, then ensure there is only one
+		// space in a row
+		String expressionRPN = String.join(" ", components).replaceAll(" +", " ");
+		
+		while (expressionRPN.charAt(0) == ' ') {
+			expressionRPN = expressionRPN.substring(1);
+		}
+		while (expressionRPN.charAt(expressionRPN.length() - 1) == ' ') {
+			expressionRPN = expressionRPN.substring(0, expressionRPN.length() - 1);
+		}
+		return expressionRPN;
+	}
+	
+	/**
+	 * Finds the position of the highest-priority operator in a list
+	 * 
+	 * @param components components to test
+	 * @param blacklist  positions of operators that should be ignored
+	 * @return position of highest priority, or -1 if the list contains no
+	 *         operators
+	 * @throws NullPointerException if components is null
+	 * @since 2019-03-22
+	 * @since v0.2.0
+	 */
+	private int findHighestPriorityOperatorPosition(
+			final List<String> components) {
+		Objects.requireNonNull(components, "components must not be null.");
+		// find highest priority
+		int maxPriority = Integer.MIN_VALUE;
+		int maxPriorityPosition = -1;
+		
+		// go over components one by one
+		// if it is an operator, test its priority to see if it's max
+		// if it is, update maxPriority and maxPriorityPosition
+		for (int i = 0; i < components.size(); i++) {
+			
+			switch (this.getTokenType(components.get(i))) {
+			case UNARY_OPERATOR:
+				final PriorityUnaryOperator<T> unaryOperator = this.unaryOperators
+						.get(components.get(i));
+				final int unaryPriority = unaryOperator.getPriority();
+				
+				if (unaryPriority > maxPriority) {
+					maxPriority = unaryPriority;
+					maxPriorityPosition = i;
+				}
+				break;
+			case BINARY_OPERATOR:
+				final PriorityBinaryOperator<T> binaryOperator = this.binaryOperators
+						.get(components.get(i));
+				final int binaryPriority = binaryOperator.getPriority();
+				
+				if (binaryPriority > maxPriority) {
+					maxPriority = binaryPriority;
+					maxPriorityPosition = i;
+				}
+				break;
+			default:
+				break;
+			}
+		}
+		
+		// max priority position found
+		return maxPriorityPosition;
+	}
+	
+	/**
+	 * Determines whether an inputted string is an object or an operator
+	 * 
+	 * @param token string to input
+	 * @return type of token it is
+	 * @throws NullPointerException if {@code expression} is null
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	private TokenType getTokenType(final String token) {
+		Objects.requireNonNull(token, "token must not be null.");
+		
+		if (this.unaryOperators.containsKey(token))
+			return TokenType.UNARY_OPERATOR;
+		else if (this.binaryOperators.containsKey(token))
+			return TokenType.BINARY_OPERATOR;
+		else
+			return TokenType.OBJECT;
+	}
+	
+	/**
+	 * Parses an expression.
+	 * 
+	 * @param expression expression to parse
+	 * @return result
+	 * @throws NullPointerException if {@code expression} is null
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	public T parseExpression(final String expression) {
+		return this.parseReversePolishExpression(
+				this.convertExpressionToReversePolish(expression));
+	}
+	
+	/**
+	 * Parses an expression expressed in reverse Polish notation.
+	 * 
+	 * @param expression expression to parse
+	 * @return result
+	 * @throws NullPointerException if {@code expression} is null
+	 * @since 2019-03-14
+	 * @since v0.2.0
+	 */
+	private T parseReversePolishExpression(final String expression) {
+		Objects.requireNonNull(expression, "expression must not be null.");
+		
+		final Deque<T> stack = new ArrayDeque<>();
+		
+		// iterate over every item in the expression, then
+		for (final String item : expression.split(" ")) {
+			// choose a path based on what kind of thing was just read
+			switch (this.getTokenType(item)) {
+			
+			case BINARY_OPERATOR:
+				if (stack.size() < 2)
+					throw new IllegalStateException(String.format(
+							"Attempted to call binary operator %s with only %d arguments.",
+							item, stack.size()));
+				
+				// get two arguments and operator, then apply!
+				final T o1 = stack.pop();
+				final T o2 = stack.pop();
+				final BinaryOperator<T> binaryOperator = this.binaryOperators
+						.get(item);
+				
+				stack.push(binaryOperator.apply(o1, o2));
+				break;
+			
+			case OBJECT:
+				// just add it to the stack
+				stack.push(this.objectObtainer.apply(item));
+				break;
+			
+			case UNARY_OPERATOR:
+				if (stack.size() < 1)
+					throw new IllegalStateException(String.format(
+							"Attempted to call unary operator %s with only %d arguments.",
+							item, stack.size()));
+				
+				// get one argument and operator, then apply!
+				final T o = stack.pop();
+				final UnaryOperator<T> unaryOperator = this.unaryOperators
+						.get(item);
+				
+				stack.push(unaryOperator.apply(o));
+				break;
+			default:
+				throw new AssertionError(
+						String.format("Internal error: Invalid token type %s.",
+								this.getTokenType(item)));
+			
+			}
+		}
+		
+		// return answer, or throw an exception if I can't
+		if (stack.size() > 1)
+			throw new IllegalStateException(
+					"Computation ended up with more than one answer.");
+		else if (stack.size() == 0)
+			throw new IllegalStateException(
+					"Computation ended up without an answer.");
+		return stack.pop();
+	}
+}
diff --git a/src/main/java/sevenUnits/math/ObjectProduct.java b/src/main/java/sevenUnits/math/ObjectProduct.java
new file mode 100644
index 0000000..db95fd4
--- /dev/null
+++ b/src/main/java/sevenUnits/math/ObjectProduct.java
@@ -0,0 +1,284 @@
+/**
+ * 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.math;
+
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.HashSet;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Set;
+import java.util.function.Function;
+
+/**
+ * An immutable product of multiple objects of a type, such as base units. The objects can be multiplied and
+ * exponentiated.
+ * 
+ * @author Adrien Hopkins
+ * @since 2019-10-16
+ */
+public final class ObjectProduct<T> {
+	/**
+	 * Returns an empty ObjectProduct of a certain type
+	 * 
+	 * @param <T>
+	 *            type of objects that can be multiplied
+	 * @return empty product
+	 * @since 2019-10-16
+	 */
+	public static final <T> ObjectProduct<T> empty() {
+		return new ObjectProduct<>(new HashMap<>());
+	}
+
+	/**
+	 * Gets an {@code ObjectProduct} from an object-to-integer mapping
+	 * 
+	 * @param <T>
+	 *            type of object in product
+	 * @param map
+	 *            map mapping objects to exponents
+	 * @return object product
+	 * @since 2019-10-16
+	 */
+	public static final <T> ObjectProduct<T> fromExponentMapping(final Map<T, Integer> map) {
+		return new ObjectProduct<>(new HashMap<>(map));
+	}
+
+	/**
+	 * Gets an ObjectProduct that has one of the inputted argument, and nothing else.
+	 * 
+	 * @param object
+	 *            object that will be in the product
+	 * @return product
+	 * @since 2019-10-16
+	 * @throws NullPointerException
+	 *             if object is null
+	 */
+	public static final <T> ObjectProduct<T> oneOf(final T object) {
+		Objects.requireNonNull(object, "object must not be null.");
+		final Map<T, Integer> map = new HashMap<>();
+		map.put(object, 1);
+		return new ObjectProduct<>(map);
+	}
+
+	/**
+	 * The objects that make up the product, mapped to their exponents. This map treats zero as null, and is immutable.
+	 * 
+	 * @since 2019-10-16
+	 */
+	final Map<T, Integer> exponents;
+
+	/**
+	 * Creates the {@code ObjectProduct}.
+	 * 
+	 * @param exponents
+	 *            objects that make up this product
+	 * @since 2019-10-16
+	 */
+	private ObjectProduct(final Map<T, Integer> exponents) {
+		this.exponents = Collections.unmodifiableMap(ConditionalExistenceCollections.conditionalExistenceMap(exponents,
+				e -> !Integer.valueOf(0).equals(e.getValue())));
+	}
+
+	/**
+	 * Calculates the quotient of two products
+	 *
+	 * @param other
+	 *            other product
+	 * @return quotient of two products
+	 * @since 2019-10-16
+	 * @throws NullPointerException
+	 *             if other is null
+	 */
+	public ObjectProduct<T> dividedBy(final ObjectProduct<T> other) {
+		Objects.requireNonNull(other, "other must not be null.");
+		// get a list of all objects in both sets
+		final Set<T> objects = new HashSet<>();
+		objects.addAll(this.getBaseSet());
+		objects.addAll(other.getBaseSet());
+
+		// get a list of all exponents
+		final Map<T, Integer> map = new HashMap<>(objects.size());
+		for (final T key : objects) {
+			map.put(key, this.getExponent(key) - other.getExponent(key));
+		}
+
+		// create the product
+		return new ObjectProduct<>(map);
+	}
+
+	// this method relies on the use of ZeroIsNullMap
+	@Override
+	public boolean equals(final Object obj) {
+		if (this == obj)
+			return true;
+		if (!(obj instanceof ObjectProduct))
+			return false;
+		final ObjectProduct<?> other = (ObjectProduct<?>) obj;
+		return Objects.equals(this.exponents, other.exponents);
+	}
+
+	/**
+	 * @return immutable map mapping objects to exponents
+	 * @since 2019-10-16
+	 */
+	public Map<T, Integer> exponentMap() {
+		return this.exponents;
+	}
+
+	/**
+	 * @return a set of all of the base objects with non-zero exponents that make up this dimension.
+	 * @since 2018-12-12
+	 * @since v0.1.0
+	 */
+	public final Set<T> getBaseSet() {
+		final Set<T> dimensions = new HashSet<>();
+
+		// add all dimensions with a nonzero exponent - zero exponents shouldn't be there in the first place
+		for (final T dimension : this.exponents.keySet()) {
+			if (!this.exponents.get(dimension).equals(0)) {
+				dimensions.add(dimension);
+			}
+		}
+
+		return dimensions;
+	}
+
+	/**
+	 * Gets the exponent for a specific dimension.
+	 * 
+	 * @param dimension
+	 *            dimension to check
+	 * @return exponent for that dimension
+	 * @since 2018-12-12
+	 * @since v0.1.0
+	 */
+	public int getExponent(final T dimension) {
+		return this.exponents.getOrDefault(dimension, 0);
+	}
+
+	@Override
+	public int hashCode() {
+		return Objects.hash(this.exponents);
+	}
+
+	/**
+	 * @return true if this product is a single object, i.e. it has one exponent of one and no other nonzero exponents
+	 * @since 2019-10-16
+	 */
+	public boolean isSingleObject() {
+		int oneCount = 0;
+		boolean twoOrMore = false; // has exponents of 2 or more
+		for (final T b : this.getBaseSet()) {
+			if (this.getExponent(b) == 1) {
+				oneCount++;
+			} else if (this.getExponent(b) != 0) {
+				twoOrMore = true;
+			}
+		}
+		return oneCount == 1 && !twoOrMore;
+	}
+
+	/**
+	 * Multiplies this product by another
+	 *
+	 * @param other
+	 *            other product
+	 * @return product of two products
+	 * @since 2019-10-16
+	 * @throws NullPointerException
+	 *             if other is null
+	 */
+	public ObjectProduct<T> times(final ObjectProduct<T> other) {
+		Objects.requireNonNull(other, "other must not be null.");
+		// get a list of all objects in both sets
+		final Set<T> objects = new HashSet<>();
+		objects.addAll(this.getBaseSet());
+		objects.addAll(other.getBaseSet());
+
+		// get a list of all exponents
+		final Map<T, Integer> map = new HashMap<>(objects.size());
+		for (final T key : objects) {
+			map.put(key, this.getExponent(key) + other.getExponent(key));
+		}
+
+		// create the product
+		return new ObjectProduct<>(map);
+	}
+
+	/**
+	 * Returns this product, but to an exponent
+	 * 
+	 * @param exponent
+	 *            exponent
+	 * @return result of exponentiation
+	 * @since 2019-10-16
+	 */
+	public ObjectProduct<T> toExponent(final int exponent) {
+		final Map<T, Integer> map = new HashMap<>(this.exponents);
+		for (final T key : this.exponents.keySet()) {
+			map.put(key, this.getExponent(key) * exponent);
+		}
+		return new ObjectProduct<>(map);
+	}
+
+	/**
+	 * Converts this product to a string using the objects' {@link Object#toString()} method. If objects have a long
+	 * toString representation, it is recommended to use {@link #toString(Function)} instead to shorten the returned
+	 * string.
+	 * 
+	 * <p>
+	 * {@inheritDoc}
+	 */
+	@Override
+	public String toString() {
+		return this.toString(Object::toString);
+	}
+
+	/**
+	 * Converts this product to a string. The objects that make up this product are represented by
+	 * {@code objectToString}
+	 * 
+	 * @param objectToString
+	 *            function to convert objects to strings
+	 * @return string representation of product
+	 * @since 2019-10-16
+	 */
+	public String toString(final Function<T, String> objectToString) {
+		final List<String> positiveStringComponents = new ArrayList<>();
+		final List<String> negativeStringComponents = new ArrayList<>();
+
+		// for each base object that makes up this object, add it and its exponent
+		for (final T object : this.getBaseSet()) {
+			final int exponent = this.exponents.get(object);
+			if (exponent > 0) {
+				positiveStringComponents.add(String.format("%s^%d", objectToString.apply(object), exponent));
+			} else if (exponent < 0) {
+				negativeStringComponents.add(String.format("%s^%d", objectToString.apply(object), -exponent));
+			}
+		}
+
+		final String positiveString = positiveStringComponents.isEmpty() ? "1"
+				: String.join(" * ", positiveStringComponents);
+		final String negativeString = negativeStringComponents.isEmpty() ? ""
+				: " / " + String.join(" * ", negativeStringComponents);
+
+		return positiveString + negativeString;
+	}
+}
diff --git a/src/main/java/sevenUnits/math/UncertainDouble.java b/src/main/java/sevenUnits/math/UncertainDouble.java
new file mode 100644
index 0000000..b81bb79
--- /dev/null
+++ b/src/main/java/sevenUnits/math/UncertainDouble.java
@@ -0,0 +1,419 @@
+/**
+ * Copyright (C) 2020 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.math;
+
+import java.math.BigDecimal;
+import java.math.RoundingMode;
+import java.util.Objects;
+import java.util.regex.Matcher;
+import java.util.regex.Pattern;
+
+/**
+ * A double with an associated uncertainty value. For example, 3.2 ± 0.2.
+ * <p>
+ * All methods in this class throw a NullPointerException if any of their
+ * arguments is null.
+ *
+ * @since 2020-09-07
+ */
+public final class UncertainDouble implements Comparable<UncertainDouble> {
+	/**
+	 * The exact value 0
+	 */
+	public static final UncertainDouble ZERO = UncertainDouble.of(0, 0);
+	
+	/**
+	 * A regular expression that can recognize toString forms
+	 */
+	private static final Pattern TO_STRING = Pattern
+			.compile("([a-zA-Z_0-9\\.\\,]+)" // a number
+					// optional "± [number]"
+					+ "(?:\\s*(?:±|\\+-)\\s*([a-zA-Z_0-9\\.\\,]+))?");
+	
+	/**
+	 * Parses a string in the form of {@link UncertainDouble#toString(boolean)}
+	 * and returns the corresponding {@code UncertainDouble} instance.
+	 * <p>
+	 * This method allows some alternative forms of the string representation,
+	 * such as using "+-" instead of "±".
+	 * 
+	 * @param s string to parse
+	 * @return {@code UncertainDouble} instance
+	 * @throws IllegalArgumentException if the string is invalid
+	 * @since 2020-09-07
+	 */
+	public static final UncertainDouble fromString(String s) {
+		Objects.requireNonNull(s, "s may not be null");
+		final Matcher matcher = TO_STRING.matcher(s);
+		
+		double value, uncertainty;
+		try {
+			value = Double.parseDouble(matcher.group(1));
+		} catch (IllegalStateException | NumberFormatException e) {
+			throw new IllegalArgumentException(
+					"String " + s + " not in correct format.");
+		}
+		
+		final String uncertaintyString = matcher.group(2);
+		if (uncertaintyString == null) {
+			uncertainty = 0;
+		} else {
+			try {
+				uncertainty = Double.parseDouble(uncertaintyString);
+			} catch (final NumberFormatException e) {
+				throw new IllegalArgumentException(
+						"String " + s + " not in correct format.");
+			}
+		}
+		
+		return UncertainDouble.of(value, uncertainty);
+	}
+	
+	/**
+	 * Gets an {@code UncertainDouble} from its value and <b>absolute</b>
+	 * uncertainty.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public static final UncertainDouble of(double value, double uncertainty) {
+		return new UncertainDouble(value, uncertainty);
+	}
+	
+	/**
+	 * Gets an {@code UncertainDouble} from its value and <b>relative</b>
+	 * uncertainty.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public static final UncertainDouble ofRelative(double value,
+			double relativeUncertainty) {
+		return new UncertainDouble(value, value * relativeUncertainty);
+	}
+	
+	private final double value;
+	
+	private final double uncertainty;
+	
+	/**
+	 * @param value
+	 * @param uncertainty
+	 * @since 2020-09-07
+	 */
+	private UncertainDouble(double value, double uncertainty) {
+		this.value = value;
+		// uncertainty should only ever be positive
+		this.uncertainty = Math.abs(uncertainty);
+	}
+	
+	/**
+	 * Compares this {@code UncertainDouble} with another
+	 * {@code UncertainDouble}.
+	 * <p>
+	 * This method only compares the values, not the uncertainties. So 3.1 ± 0.5
+	 * is considered less than 3.2 ± 0.5, even though they are equivalent.
+	 * <p>
+	 * <b>Note:</b> The natural ordering of this class is inconsistent with
+	 * equals. Specifically, if two {@code UncertainDouble} instances {@code a}
+	 * and {@code b} have the same value but different uncertainties,
+	 * {@code a.compareTo(b)} will return 0 but {@code a.equals(b)} will return
+	 * {@code false}.
+	 */
+	@Override
+	public final int compareTo(UncertainDouble o) {
+		return Double.compare(this.value, o.value);
+	}
+	
+	/**
+	 * Returns the quotient of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble dividedBy(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.ofRelative(this.value / other.value, Math
+				.hypot(this.relativeUncertainty(), other.relativeUncertainty()));
+	}
+	
+	/**
+	 * Returns the quotient of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble dividedByExact(double other) {
+		return UncertainDouble.of(this.value / other, this.uncertainty / other);
+	}
+	
+	@Override
+	public final boolean equals(Object obj) {
+		if (this == obj)
+			return true;
+		if (!(obj instanceof UncertainDouble))
+			return false;
+		final UncertainDouble other = (UncertainDouble) obj;
+		if (Double.compare(this.value, other.value) != 0)
+			return false;
+		if (Double.compare(this.uncertainty, other.uncertainty) != 0)
+			return false;
+		return true;
+	}
+	
+	/**
+	 * @param other another {@code UncertainDouble}
+	 * @return true iff this and {@code other} are within each other's
+	 *         uncertainty range.
+	 * @since 2020-09-07
+	 */
+	public final boolean equivalent(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return Math.abs(this.value - other.value) <= Math.min(this.uncertainty,
+				other.uncertainty);
+	}
+	
+	/**
+	 * Gets the preferred scale for rounding a value for toString.
+	 * 
+	 * @since 2020-09-07
+	 */
+	private final int getDisplayScale() {
+		// round based on uncertainty
+		// if uncertainty starts with 1 (ignoring zeroes and the decimal
+		// point), rounds
+		// so that uncertainty has 2 significant digits.
+		// otherwise, rounds so that uncertainty has 1 significant digits.
+		// the value is rounded to the same number of decimal places as the
+		// uncertainty.
+		final BigDecimal bigUncertainty = BigDecimal.valueOf(this.uncertainty);
+		
+		// the scale that will give the uncertainty two decimal places
+		final int twoDecimalPlacesScale = bigUncertainty.scale()
+				- bigUncertainty.precision() + 2;
+		final BigDecimal roundedUncertainty = bigUncertainty
+				.setScale(twoDecimalPlacesScale, RoundingMode.HALF_EVEN);
+		
+		if (roundedUncertainty.unscaledValue().intValue() >= 20)
+			return twoDecimalPlacesScale - 1; // one decimal place
+		else
+			return twoDecimalPlacesScale;
+	}
+	
+	@Override
+	public final int hashCode() {
+		final int prime = 31;
+		int result = 1;
+		result = prime * result + Double.hashCode(this.value);
+		result = prime * result + Double.hashCode(this.uncertainty);
+		return result;
+	}
+	
+	/**
+	 * @return true iff the value has no uncertainty
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final boolean isExact() {
+		return this.uncertainty == 0;
+	}
+	
+	/**
+	 * Returns the difference of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble minus(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.of(this.value - other.value,
+				Math.hypot(this.uncertainty, other.uncertainty));
+	}
+	
+	/**
+	 * Returns the difference of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble minusExact(double other) {
+		return UncertainDouble.of(this.value - other, this.uncertainty);
+	}
+	
+	/**
+	 * Returns the sum of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble plus(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.of(this.value + other.value,
+				Math.hypot(this.uncertainty, other.uncertainty));
+	}
+	
+	/**
+	 * Returns the sum of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble plusExact(double other) {
+		return UncertainDouble.of(this.value + other, this.uncertainty);
+	}
+	
+	/**
+	 * @return relative uncertainty
+	 * @since 2020-09-07
+	 */
+	public final double relativeUncertainty() {
+		return this.uncertainty / this.value;
+	}
+	
+	/**
+	 * Returns the product of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble times(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.ofRelative(this.value * other.value, Math
+				.hypot(this.relativeUncertainty(), other.relativeUncertainty()));
+	}
+	
+	/**
+	 * Returns the product of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble timesExact(double other) {
+		return UncertainDouble.of(this.value * other, this.uncertainty * other);
+	}
+	
+	/**
+	 * Returns the result of {@code this} raised to the exponent {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble toExponent(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		
+		final double result = Math.pow(this.value, other.value);
+		final double relativeUncertainty = Math.hypot(
+				other.value * this.relativeUncertainty(),
+				Math.log(this.value) * other.uncertainty);
+		
+		return UncertainDouble.ofRelative(result, relativeUncertainty);
+	}
+	
+	/**
+	 * Returns the result of {@code this} raised the exact exponent
+	 * {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble toExponentExact(double other) {
+		return UncertainDouble.ofRelative(Math.pow(this.value, other),
+				this.relativeUncertainty() * other);
+	}
+	
+	/**
+	 * Returns a string representation of this {@code UncertainDouble}.
+	 * <p>
+	 * This method returns the same value as {@link #toString(boolean)}, but
+	 * {@code showUncertainty} is true if and only if the uncertainty is
+	 * non-zero.
+	 * 
+	 * <p>
+	 * Examples:
+	 * 
+	 * <pre>
+	 * UncertainDouble.of(3.27, 0.22).toString() = "3.3 ± 0.2"
+	 * UncertainDouble.of(3.27, 0.13).toString() = "3.27 ± 0.13"
+	 * UncertainDouble.of(-5.01, 0).toString() = "-5.01"
+	 * </pre>
+	 * 
+	 * @since 2020-09-07
+	 */
+	@Override
+	public final String toString() {
+		return this.toString(!this.isExact());
+	}
+	
+	/**
+	 * Returns a string representation of this {@code UncertainDouble}.
+	 * <p>
+	 * If {@code showUncertainty} is true, the string will be of the form "VALUE
+	 * ± UNCERTAINTY", and if it is false the string will be of the form "VALUE"
+	 * <p>
+	 * VALUE represents a string representation of this {@code UncertainDouble}'s
+	 * value. If the uncertainty is non-zero, the string will be rounded to the
+	 * same precision as the uncertainty, otherwise it will not be rounded. The
+	 * string is still rounded if {@code showUncertainty} is false.<br>
+	 * UNCERTAINTY represents a string representation of this
+	 * {@code UncertainDouble}'s uncertainty. If the uncertainty ends in 1X
+	 * (where X represents any digit) it will be rounded to two significant
+	 * digits otherwise it will be rounded to one significant digit.
+	 * <p>
+	 * Examples:
+	 * 
+	 * <pre>
+	 * UncertainDouble.of(3.27, 0.22).toString(false) = "3.3"
+	 * UncertainDouble.of(3.27, 0.22).toString(true) = "3.3 ± 0.2"
+	 * UncertainDouble.of(3.27, 0.13).toString(false) = "3.27"
+	 * UncertainDouble.of(3.27, 0.13).toString(true) = "3.27 ± 0.13"
+	 * UncertainDouble.of(-5.01, 0).toString(false) = "-5.01"
+	 * UncertainDouble.of(-5.01, 0).toString(true) = "-5.01 ± 0.0"
+	 * </pre>
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final String toString(boolean showUncertainty) {
+		String valueString, uncertaintyString;
+		
+		// generate the string representation of value and uncertainty
+		if (this.isExact()) {
+			uncertaintyString = "0.0";
+			valueString = Double.toString(this.value);
+			
+		} else {
+			// round the value and uncertainty according to getDisplayScale()
+			final BigDecimal bigValue = BigDecimal.valueOf(this.value);
+			final BigDecimal bigUncertainty = BigDecimal.valueOf(this.uncertainty);
+			
+			final int displayScale = this.getDisplayScale();
+			final BigDecimal roundedUncertainty = bigUncertainty
+					.setScale(displayScale, RoundingMode.HALF_EVEN);
+			final BigDecimal roundedValue = bigValue.setScale(displayScale,
+					RoundingMode.HALF_EVEN);
+			
+			valueString = roundedValue.toString();
+			uncertaintyString = roundedUncertainty.toString();
+		}
+		
+		// return "value" or "value ± uncertainty" depending on showUncertainty
+		return valueString + (showUncertainty ? " ± " + uncertaintyString : "");
+	}
+	
+	/**
+	 * @return absolute uncertainty
+	 * @since 2020-09-07
+	 */
+	public final double uncertainty() {
+		return this.uncertainty;
+	}
+	
+	/**
+	 * @return value without uncertainty
+	 * @since 2020-09-07
+	 */
+	public final double value() {
+		return this.value;
+	}
+}
diff --git a/src/main/java/sevenUnits/math/package-info.java b/src/main/java/sevenUnits/math/package-info.java
new file mode 100644
index 0000000..62f72cd
--- /dev/null
+++ b/src/main/java/sevenUnits/math/package-info.java
@@ -0,0 +1,24 @@
+/**
+ * Copyright (C) 2019 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/>.
+ */
+/**
+ * Supplementary classes that are not related to units, but are necessary for their function.
+ * 
+ * @author Adrien Hopkins
+ * @since 2019-03-14
+ * @since v0.2.0
+ */
+package sevenUnits.math;
\ No newline at end of file