/**
 * 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.utils;

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;
	}
}