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/**
* 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 org.unitConverter.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();
}
}
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