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+/**
+ * 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 org.unitConverter.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;
+	}
+}