Allow fractional exponents

6 files changed, 139 insertions, 94 deletions

diff --git a/docs/roadmap.org b/docs/roadmap.org
index 5a3888f..bd0ccee 100644
--- a/docs/roadmap.org
+++ b/docs/roadmap.org
@@ -8,7 +8,6 @@ Feature Requirements:
   (It should not be required to handle features that aren't in 7Units; those definitions should be ignored with a warning)
 - 7Units's expression converter should support most or all of the conversion features supported by GNU Units:
   - Converting to sums of units (it should also be possible to do this in the unit converter with preset combinations)
-  - Non-integer exponents
   - (/Optional/) Inverse nonlinear conversion with the tilde prefix
   - (/Optional/) Nonlinear units should be specifiable in unit files.
   - /Any other feature not listed should be considered optional./
diff --git a/src/main/java/sevenUnits/unit/LinearUnit.java b/src/main/java/sevenUnits/unit/LinearUnit.java
index 6489229..a230f28 100644
--- a/src/main/java/sevenUnits/unit/LinearUnit.java
+++ b/src/main/java/sevenUnits/unit/LinearUnit.java
@@ -46,7 +46,7 @@ public final class LinearUnit extends Unit {
 				Objects.requireNonNull(unit, "unit must not be null.").getBase(),
 				unit.convertToBase(value), NameSymbol.EMPTY);
 	}
-
+	
 	/**
 	 * Gets a {@code LinearUnit} from a unit and a value. For example, converts
 	 * '59 °F' to a linear unit with the value of '288.15 K'
@@ -64,7 +64,7 @@ public final class LinearUnit extends Unit {
 				Objects.requireNonNull(unit, "unit must not be null.").getBase(),
 				unit.convertToBase(value), ns);
 	}
-
+	
 	/**
 	 * @return the base unit associated with {@code unit}, as a
 	 *         {@code LinearUnit}.
@@ -73,7 +73,7 @@ public final class LinearUnit extends Unit {
 	public static LinearUnit getBase(final Unit unit) {
 		return new LinearUnit(unit.getBase(), 1, NameSymbol.EMPTY);
 	}
-
+	
 	/**
 	 * @return the base unit associated with {@code unitlike}, as a
 	 *         {@code LinearUnit}.
@@ -82,7 +82,7 @@ public final class LinearUnit extends Unit {
 	public static LinearUnit getBase(final Unitlike<?> unit) {
 		return new LinearUnit(unit.getBase(), 1, NameSymbol.EMPTY);
 	}
-
+	
 	/**
 	 * Gets a {@code LinearUnit} from a unit base and a conversion factor. In
 	 * other words, gets the product of {@code unitBase} and
@@ -98,7 +98,7 @@ public final class LinearUnit extends Unit {
 			final double conversionFactor) {
 		return new LinearUnit(unitBase, conversionFactor, NameSymbol.EMPTY);
 	}
-
+	
 	/**
 	 * Gets a {@code LinearUnit} from a unit base and a conversion factor. In
 	 * other words, gets the product of {@code unitBase} and
@@ -115,7 +115,7 @@ public final class LinearUnit extends Unit {
 			final double conversionFactor, final NameSymbol ns) {
 		return new LinearUnit(unitBase, conversionFactor, ns);
 	}
-
+	
 	/**
 	 * The value of this unit as represented in its base form. Mathematically,
 	 * 
@@ -126,7 +126,7 @@ public final class LinearUnit extends Unit {
 	 * @since 2019-10-16
 	 */
 	private final double conversionFactor;
-
+	
 	/**
 	 * Creates the {@code LinearUnit}.
 	 * 
@@ -139,7 +139,7 @@ public final class LinearUnit extends Unit {
 		super(unitBase, ns);
 		this.conversionFactor = conversionFactor;
 	}
-
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -149,7 +149,7 @@ public final class LinearUnit extends Unit {
 	protected double convertFromBase(final double value) {
 		return value / this.getConversionFactor();
 	}
-
+	
 	/**
 	 * Converts an {@code UncertainDouble} value expressed in this unit to an
 	 * {@code UncertainValue} value expressed in {@code other}.
@@ -172,9 +172,9 @@ public final class LinearUnit extends Unit {
 		else
 			throw new IllegalArgumentException(
 					String.format("Cannot convert from %s to %s.", this, other));
-
+		
 	}
-
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -184,7 +184,7 @@ public final class LinearUnit extends Unit {
 	protected double convertToBase(final double value) {
 		return value * this.getConversionFactor();
 	}
-
+	
 	/**
 	 * Converts an {@code UncertainDouble} to the base unit.
 	 * 
@@ -193,7 +193,7 @@ public final class LinearUnit extends Unit {
 	UncertainDouble convertToBase(final UncertainDouble value) {
 		return value.timesExact(this.getConversionFactor());
 	}
-
+	
 	/**
 	 * Divides this unit by a scalar.
 	 * 
@@ -205,7 +205,7 @@ public final class LinearUnit extends Unit {
 	public LinearUnit dividedBy(final double divisor) {
 		return valueOf(this.getBase(), this.getConversionFactor() / divisor);
 	}
-
+	
 	/**
 	 * Returns the quotient of this unit and another.
 	 * 
@@ -217,14 +217,14 @@ public final class LinearUnit extends Unit {
 	 */
 	public LinearUnit dividedBy(final LinearUnit divisor) {
 		Objects.requireNonNull(divisor, "other must not be null");
-
+		
 		// divide the units
 		final ObjectProduct<BaseUnit> base = this.getBase()
 				.dividedBy(divisor.getBase());
 		return valueOf(base,
 				this.getConversionFactor() / divisor.getConversionFactor());
 	}
-
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -239,7 +239,7 @@ public final class LinearUnit extends Unit {
 				&& DecimalComparison.equals(this.getConversionFactor(),
 						other.getConversionFactor());
 	}
-
+	
 	/**
 	 * @return conversion factor
 	 * @since 2019-10-16
@@ -247,7 +247,7 @@ public final class LinearUnit extends Unit {
 	public double getConversionFactor() {
 		return this.conversionFactor;
 	}
-
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -258,7 +258,7 @@ public final class LinearUnit extends Unit {
 		return 31 * this.getBase().hashCode()
 				+ DecimalComparison.hash(this.getConversionFactor());
 	}
-
+	
 	/**
 	 * @return whether this unit is equivalent to a {@code BaseUnit} (i.e. there
 	 *         is a {@code BaseUnit b} where
@@ -268,7 +268,7 @@ public final class LinearUnit extends Unit {
 	public boolean isBase() {
 		return this.isCoherent() && this.getBase().isSingleObject();
 	}
-
+	
 	/**
 	 * @return whether this unit is coherent (i.e. has conversion factor 1)
 	 * @since 2019-10-16
@@ -276,7 +276,7 @@ public final class LinearUnit extends Unit {
 	public boolean isCoherent() {
 		return this.getConversionFactor() == 1;
 	}
-
+	
 	/**
 	 * Returns the difference of this unit and another.
 	 * <p>
@@ -296,18 +296,18 @@ public final class LinearUnit extends Unit {
 	 */
 	public LinearUnit minus(final LinearUnit subtrahend) {
 		Objects.requireNonNull(subtrahend, "addend must not be null.");
-
+		
 		// reject subtrahends that cannot be added to this unit
 		if (!this.getBase().equals(subtrahend.getBase()))
 			throw new IllegalArgumentException(String.format(
 					"Incompatible units for subtraction \"%s\" and \"%s\".", this,
 					subtrahend));
-
+		
 		// subtract the units
 		return valueOf(this.getBase(),
 				this.getConversionFactor() - subtrahend.getConversionFactor());
 	}
-
+	
 	/**
 	 * Returns the sum of this unit and another.
 	 * <p>
@@ -327,18 +327,18 @@ public final class LinearUnit extends Unit {
 	 */
 	public LinearUnit plus(final LinearUnit addend) {
 		Objects.requireNonNull(addend, "addend must not be null.");
-
+		
 		// reject addends that cannot be added to this unit
 		if (!this.getBase().equals(addend.getBase()))
 			throw new IllegalArgumentException(String.format(
 					"Incompatible units for addition \"%s\" and \"%s\".", this,
 					addend));
-
+		
 		// add the units
 		return valueOf(this.getBase(),
 				this.getConversionFactor() + addend.getConversionFactor());
 	}
-
+	
 	/**
 	 * Multiplies this unit by a scalar.
 	 * 
@@ -350,7 +350,7 @@ public final class LinearUnit extends Unit {
 	public LinearUnit times(final double multiplier) {
 		return valueOf(this.getBase(), this.getConversionFactor() * multiplier);
 	}
-
+	
 	/**
 	 * Returns the product of this unit and another.
 	 * 
@@ -362,21 +362,21 @@ public final class LinearUnit extends Unit {
 	 */
 	public LinearUnit times(final LinearUnit multiplier) {
 		Objects.requireNonNull(multiplier, "other must not be null");
-
+		
 		// multiply the units
 		final ObjectProduct<BaseUnit> base = this.getBase()
 				.times(multiplier.getBase());
 		return valueOf(base,
 				this.getConversionFactor() * multiplier.getConversionFactor());
 	}
-
+	
 	@Override
 	public String toDefinitionString() {
 		return Double.toString(this.conversionFactor)
 				+ (this.getBase().equals(ObjectProduct.empty()) ? ""
 						: " " + this.getBase().toString(BaseUnit::getShortName));
 	}
-
+	
 	/**
 	 * Returns this unit but to an exponent.
 	 * 
@@ -389,12 +389,24 @@ public final class LinearUnit extends Unit {
 		return valueOf(this.getBase().toExponent(exponent),
 				Math.pow(this.conversionFactor, exponent));
 	}
-
+	
+	/**
+	 * Returns this unit to an exponent, rounding the resulting dimensions to the
+	 * nearest integer.
+	 *
+	 * @since 2024-08-22
+	 * @see ObjectProduct#toExponentRounded
+	 */
+	public LinearUnit toExponentRounded(final double exponent) {
+		return valueOf(this.getBase().toExponentRounded(exponent),
+				Math.pow(this.conversionFactor, exponent));
+	}
+	
 	@Override
 	public LinearUnit withName(final NameSymbol ns) {
 		return valueOf(this.getBase(), this.getConversionFactor(), ns);
 	}
-
+	
 	/**
 	 * Returns the result of applying {@code prefix} to this unit.
 	 * <p>
@@ -413,7 +425,7 @@ public final class LinearUnit extends Unit {
 	 */
 	public LinearUnit withPrefix(final UnitPrefix prefix) {
 		final LinearUnit unit = this.times(prefix.getMultiplier());
-
+		
 		// create new name and symbol, if possible
 		final String name;
 		if (this.getPrimaryName().isPresent()
@@ -422,14 +434,14 @@ public final class LinearUnit extends Unit {
 		} else {
 			name = null;
 		}
-
+		
 		final String symbol;
 		if (this.getSymbol().isPresent() && prefix.getSymbol().isPresent()) {
 			symbol = prefix.getSymbol().get() + this.getSymbol().get();
 		} else {
 			symbol = null;
 		}
-
+		
 		return unit.withName(NameSymbol.ofNullable(name, symbol));
 	}
 }
diff --git a/src/main/java/sevenUnits/unit/LinearUnitValue.java b/src/main/java/sevenUnits/unit/LinearUnitValue.java
index fad3eb0..db2936c 100644
--- a/src/main/java/sevenUnits/unit/LinearUnitValue.java
+++ b/src/main/java/sevenUnits/unit/LinearUnitValue.java
@@ -338,6 +338,17 @@ public final class LinearUnitValue {
 				this.value.toExponentExact(exponent));
 	}
 	
+	/**
+	 * Raises this value to an exponent, rounding all dimensions to integers.
+	 *
+	 * @since 2024-08-22
+	 * @see ObjectProduct#toExponentRounded
+	 */
+	public LinearUnitValue toExponentRounded(final double exponent) {
+		return LinearUnitValue.of(this.unit.toExponentRounded(exponent),
+				this.value.toExponentExact(exponent));
+	}
+	
 	@Override
 	public String toString() {
 		return this.toString(!this.value.isExact(), RoundingMode.HALF_EVEN);
diff --git a/src/main/java/sevenUnits/unit/UnitDatabase.java b/src/main/java/sevenUnits/unit/UnitDatabase.java
index 05c31c4..514b27d 100644
--- a/src/main/java/sevenUnits/unit/UnitDatabase.java
+++ b/src/main/java/sevenUnits/unit/UnitDatabase.java
@@ -44,7 +44,6 @@ 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.NameSymbol;
 import sevenUnits.utils.ObjectProduct;
@@ -1117,20 +1116,13 @@ public final class UnitDatabase {
 	 */
 	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.");
+		if (!exponentUnit.getBase().equals(Metric.ONE.getBase()))
+			throw new IllegalArgumentException(String.format(
+					"Tried to exponentiate %s^%s, but exponents must be dimensionless numbers.",
+					base, exponentUnit));
+		
+		final double exponent = exponentUnit.getConversionFactor();
+		return base.toExponentRounded(exponent);
 	}
 	
 	/**
@@ -1143,20 +1135,13 @@ public final class UnitDatabase {
 	 */
 	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.");
+		if (!exponentValue.canConvertTo(Metric.ONE))
+			throw new IllegalArgumentException(String.format(
+					"Tried to exponentiate %s^%s, but exponents must be dimensionless numbers.",
+					base, exponentValue));
+		
+		final double exponent = exponentValue.getValueExact();
+		return base.toExponentRounded(exponent);
 	}
 	
 	/**
diff --git a/src/main/java/sevenUnits/utils/ObjectProduct.java b/src/main/java/sevenUnits/utils/ObjectProduct.java
index 5a29d79..4ed70be 100644
--- a/src/main/java/sevenUnits/utils/ObjectProduct.java
+++ b/src/main/java/sevenUnits/utils/ObjectProduct.java
@@ -35,6 +35,12 @@ import java.util.function.Function;
  */
 public class ObjectProduct<T> implements Nameable {
 	/**
+	 * If {@link #toExponentRounded}'s rounding changes exponents by more than
+	 * this value, a warning will be printed to standard error.
+	 */
+	private static final double ROUND_WARN_THRESHOLD = 1e-12;
+	
+	/**
 	 * Returns an empty ObjectProduct of a certain type
 	 * 
 	 * @param <T> type of objects that can be multiplied
@@ -44,7 +50,7 @@ public class ObjectProduct<T> implements Nameable {
 	public static final <T> ObjectProduct<T> empty() {
 		return new ObjectProduct<>(new HashMap<>());
 	}
-
+	
 	/**
 	 * Gets an {@code ObjectProduct} from an object-to-integer mapping
 	 * 
@@ -57,7 +63,7 @@ public class ObjectProduct<T> implements Nameable {
 			final Map<T, Integer> map) {
 		return new ObjectProduct<>(new HashMap<>(map));
 	}
-
+	
 	/**
 	 * Gets an ObjectProduct that has one of the inputted argument, and nothing
 	 * else.
@@ -73,7 +79,7 @@ public class ObjectProduct<T> implements Nameable {
 		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.
@@ -81,12 +87,12 @@ public class ObjectProduct<T> implements Nameable {
 	 * @since 2019-10-16
 	 */
 	final Map<T, Integer> exponents;
-
+	
 	/**
 	 * The object's name and symbol
 	 */
 	private final NameSymbol nameSymbol;
-
+	
 	/**
 	 * Creates a {@code ObjectProduct} without a name/symbol.
 	 * 
@@ -96,7 +102,7 @@ public class ObjectProduct<T> implements Nameable {
 	ObjectProduct(final Map<T, Integer> exponents) {
 		this(exponents, NameSymbol.EMPTY);
 	}
-
+	
 	/**
 	 * Creates the {@code ObjectProduct}.
 	 * 
@@ -110,7 +116,7 @@ public class ObjectProduct<T> implements Nameable {
 						e -> !Integer.valueOf(0).equals(e.getValue())));
 		this.nameSymbol = nameSymbol;
 	}
-
+	
 	/**
 	 * Calculates the quotient of two products
 	 *
@@ -125,17 +131,17 @@ public class ObjectProduct<T> implements Nameable {
 		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) {
@@ -146,7 +152,7 @@ public class ObjectProduct<T> implements Nameable {
 		final ObjectProduct<?> other = (ObjectProduct<?>) obj;
 		return Objects.equals(this.exponents, other.exponents);
 	}
-
+	
 	/**
 	 * @return immutable map mapping objects to exponents
 	 * @since 2019-10-16
@@ -154,7 +160,7 @@ public class ObjectProduct<T> implements Nameable {
 	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.
@@ -163,7 +169,7 @@ public class ObjectProduct<T> implements Nameable {
 	 */
 	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()) {
@@ -171,10 +177,10 @@ public class ObjectProduct<T> implements Nameable {
 				dimensions.add(dimension);
 			}
 		}
-
+		
 		return dimensions;
 	}
-
+	
 	/**
 	 * Gets the exponent for a specific dimension.
 	 * 
@@ -186,17 +192,17 @@ public class ObjectProduct<T> implements Nameable {
 	public int getExponent(final T dimension) {
 		return this.exponents.getOrDefault(dimension, 0);
 	}
-
+	
 	@Override
 	public NameSymbol getNameSymbol() {
 		return this.nameSymbol;
 	}
-
+	
 	@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
@@ -214,7 +220,7 @@ public class ObjectProduct<T> implements Nameable {
 		}
 		return oneCount == 1 && !twoOrMore;
 	}
-
+	
 	/**
 	 * Multiplies this product by another
 	 *
@@ -229,17 +235,17 @@ public class ObjectProduct<T> implements Nameable {
 		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
 	 * 
@@ -254,7 +260,32 @@ public class ObjectProduct<T> implements Nameable {
 		}
 		return new ObjectProduct<>(map);
 	}
-
+	
+	/**
+	 * Returns this product to an exponent, where every dimension is rounded to
+	 * the nearest integer.
+	 * 
+	 * This function will send a warning (via {@link System.err}) if the rounding
+	 * significantly changes the value.
+	 *
+	 * @since 2024-08-22
+	 */
+	public ObjectProduct<T> toExponentRounded(final double exponent) {
+		final Map<T, Integer> map = new HashMap<>(this.exponents);
+		for (final T key : this.exponents.keySet()) {
+			final double newExponent = this.getExponent(key) * exponent;
+			if (Math.abs(
+					newExponent - Math.round(newExponent)) > ROUND_WARN_THRESHOLD) {
+				System.err.printf(
+						"Exponent Rounding Warning: Dimension exponents must be integers, so %d ^ %g = %g was rounded to %d.\n",
+						this.getExponent(key), exponent, newExponent,
+						Math.round(newExponent));
+			}
+			map.put(key, (int) Math.round(newExponent));
+		}
+		return new ObjectProduct<>(map);
+	}
+	
 	/**
 	 * Converts this product to a string using the objects'
 	 * {@link Object#toString()} method (or {@link Nameable#getShortName} if
@@ -271,7 +302,7 @@ public class ObjectProduct<T> implements Nameable {
 				.toString(o -> o instanceof Nameable ? ((Nameable) o).getShortName()
 						: o.toString());
 	}
-
+	
 	/**
 	 * Converts this product to a string. The objects that make up this product
 	 * are represented by {@code objectToString}
@@ -283,7 +314,7 @@ public class ObjectProduct<T> implements Nameable {
 	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);
@@ -297,15 +328,15 @@ public class ObjectProduct<T> implements Nameable {
 						objectToString.apply(object), -exponent));
 			}
 		}
-
+		
 		final String positiveString = positiveStringComponents.isEmpty() ? "1"
 				: String.join(" * ", positiveStringComponents);
 		final String negativeString = negativeStringComponents.isEmpty() ? ""
 				: " / " + String.join(" * ", negativeStringComponents);
-
+		
 		return positiveString + negativeString;
 	}
-
+	
 	/**
 	 * @return named version of this {@code ObjectProduct}, using data from
 	 *         {@code nameSymbol}
diff --git a/src/main/resources/unitsfile.txt b/src/main/resources/unitsfile.txt
index ecd9bb6..dc33abd 100644
--- a/src/main/resources/unitsfile.txt
+++ b/src/main/resources/unitsfile.txt
@@ -165,6 +165,7 @@ gregorianyear			365.2425 day
 gregorianmonth          gregorianyear / 12
 
 # Other non-SI "metric" units
+are						100 m^2
 litre					0.001 m^3
 liter					litre
 l						litre
@@ -188,11 +189,17 @@ inch					foot / 12
 in						inch
 yard					3 foot
 yd						yard
+chain					66 ft
+ch						chain
+furlong					10 chain
 mile					1760 yard
 mi						mile
 ftin					foot; inch
 ydftin					yard; foot; inch
 
+# Imperial area units
+acre					chain * furlong
+
 # Compressed notation
 kph						km / hour
 mph						mile / hour