/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.lucene.util;
import java.math.BigInteger;
/**
* Math static utility methods.
*/
public final class MathUtil {
// No instance:
private MathUtil() {
}
/**
* Returns {@code x <= 0 ? 0 : Math.floor(Math.log(x) / Math.log(base))}
* @param base must be {@code > 1}
*/
public static int log(long x, int base) {
if (base <= 1) {
throw new IllegalArgumentException("base must be > 1");
}
int ret = 0;
while (x >= base) {
x /= base;
ret++;
}
return ret;
}
/**
* Calculates logarithm in a given base with doubles.
*/
public static double log(double base, double x) {
return Math.log(x) / Math.log(base);
}
/** Return the greatest common divisor of <code>a</code> and <code>b</code>,
* consistently with {@link BigInteger#gcd(BigInteger)}.
* <p><b>NOTE</b>: A greatest common divisor must be positive, but
* <code>2^64</code> cannot be expressed as a long although it
* is the GCD of {@link Long#MIN_VALUE} and <code>0</code> and the GCD of
* {@link Long#MIN_VALUE} and {@link Long#MIN_VALUE}. So in these 2 cases,
* and only them, this method will return {@link Long#MIN_VALUE}. */
// see http://en.wikipedia.org/wiki/Binary_GCD_algorithm#Iterative_version_in_C.2B.2B_using_ctz_.28count_trailing_zeros.29
public static long gcd(long a, long b) {
a = Math.abs(a);
b = Math.abs(b);
if (a == 0) {
return b;
} else if (b == 0) {
return a;
}
final int commonTrailingZeros = Long.numberOfTrailingZeros(a | b);
a >>>= Long.numberOfTrailingZeros(a);
while (true) {
b >>>= Long.numberOfTrailingZeros(b);
if (a == b) {
break;
} else if (a > b || a == Long.MIN_VALUE) { // MIN_VALUE is treated as 2^64
final long tmp = a;
a = b;
b = tmp;
}
if (a == 1) {
break;
}
b -= a;
}
return a << commonTrailingZeros;
}
/**
* Calculates inverse hyperbolic sine of a {@code double} value.
* <p>
* Special cases:
* <ul>
* <li>If the argument is NaN, then the result is NaN.
* <li>If the argument is zero, then the result is a zero with the same sign as the argument.
* <li>If the argument is infinite, then the result is infinity with the same sign as the argument.
* </ul>
*/
public static double asinh(double a) {
final double sign;
// check the sign bit of the raw representation to handle -0
if (Double.doubleToRawLongBits(a) < 0) {
a = Math.abs(a);
sign = -1.0d;
} else {
sign = 1.0d;
}
return sign * Math.log(Math.sqrt(a * a + 1.0d) + a);
}
/**
* Calculates inverse hyperbolic cosine of a {@code double} value.
* <p>
* Special cases:
* <ul>
* <li>If the argument is NaN, then the result is NaN.
* <li>If the argument is +1, then the result is a zero.
* <li>If the argument is positive infinity, then the result is positive infinity.
* <li>If the argument is less than 1, then the result is NaN.
* </ul>
*/
public static double acosh(double a) {
return Math.log(Math.sqrt(a * a - 1.0d) + a);
}
/**
* Calculates inverse hyperbolic tangent of a {@code double} value.
* <p>
* Special cases:
* <ul>
* <li>If the argument is NaN, then the result is NaN.
* <li>If the argument is zero, then the result is a zero with the same sign as the argument.
* <li>If the argument is +1, then the result is positive infinity.
* <li>If the argument is -1, then the result is negative infinity.
* <li>If the argument's absolute value is greater than 1, then the result is NaN.
* </ul>
*/
public static double atanh(double a) {
final double mult;
// check the sign bit of the raw representation to handle -0
if (Double.doubleToRawLongBits(a) < 0) {
a = Math.abs(a);
mult = -0.5d;
} else {
mult = 0.5d;
}
return mult * Math.log((1.0d + a) / (1.0d - a));
}
}