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/*
* 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 == 2) {
// This specialized method is 30x faster.
return x <= 0 ? 0 : 63 - Long.numberOfLeadingZeros(x);
} else 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 a and b, consistently with
* {@link BigInteger#gcd(BigInteger)}.
*
* NOTE: A greatest common divisor must be positive, but 2^64 cannot be
* expressed as a long although it is the GCD of {@link Long#MIN_VALUE} and 0 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.
*
*
Special cases:
*
*
* - If the argument is NaN, then the result is NaN.
*
- If the argument is zero, then the result is a zero with the same sign as the argument.
*
- If the argument is infinite, then the result is infinity with the same sign as the
* argument.
*
*/
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.
*
* Special cases:
*
*
* - If the argument is NaN, then the result is NaN.
*
- If the argument is +1, then the result is a zero.
*
- If the argument is positive infinity, then the result is positive infinity.
*
- If the argument is less than 1, then the result is NaN.
*
*/
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.
*
* Special cases:
*
*
* - If the argument is NaN, then the result is NaN.
*
- If the argument is zero, then the result is a zero with the same sign as the argument.
*
- If the argument is +1, then the result is positive infinity.
*
- If the argument is -1, then the result is negative infinity.
*
- If the argument's absolute value is greater than 1, then the result is NaN.
*
*/
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));
}
/**
* Return a relative error bound for a sum of {@code numValues} positive doubles, computed using
* recursive summation, ie. sum = x1 + ... + xn. NOTE: This only works if all values are POSITIVE
* so that Σ |xi| == |Σ xi|. This uses formula 3.5 from Higham, Nicholas J. (1993), "The accuracy
* of floating point summation", SIAM Journal on Scientific Computing.
*/
public static double sumRelativeErrorBound(int numValues) {
if (numValues <= 1) {
return 0;
}
// u = unit roundoff in the paper, also called machine precision or machine epsilon
double u = Math.scalb(1.0, -52);
return (numValues - 1) * u;
}
/**
* Return the maximum possible sum across {@code numValues} non-negative doubles, assuming one sum
* yielded {@code sum}.
*
* @see #sumRelativeErrorBound(int)
*/
public static double sumUpperBound(double sum, int numValues) {
if (numValues <= 2) {
// When there are only two clauses, the sum is always the same regardless
// of the order.
return sum;
}
// The error of sums depends on the order in which values are summed up. In
// order to avoid this issue, we compute an upper bound of the value that
// the sum may take. If the max relative error is b, then it means that two
// sums are always within 2*b of each other.
// For conjunctions, we could skip this error factor since the order in which
// scores are summed up is predictable, but in practice, this wouldn't help
// much since the delta that is introduced by this error factor is usually
// cancelled by the float cast.
double b = MathUtil.sumRelativeErrorBound(numValues);
return (1.0 + 2 * b) * sum;
}
}