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/*
* This file is part of choco-solver, http://choco-solver.org/
*
* Copyright (c) 2024, IMT Atlantique. All rights reserved.
*
* Licensed under the BSD 4-clause license.
*
* See LICENSE file in the project root for full license information.
*/
package org.chocosolver.util.tools;
/**
* various mathematics utilities. The functions do not exist in the basic math package Math.*
*
* @author Charles Prud'homme, Arnaud Malapert
* @version 2.0.1
* @since 8 dec. 2008 version 2.0.1
*/
public final class MathUtils {
/**
* Precision for rounded logarithm.
*/
public final static double ROUNDED_LOG_PRECISION = 10000;
public final static double LOG10_2 = Math.log10(2);
private MathUtils() {
//do nothing
}
/**
* simple recursive version of factorial
* @param n size of the suite
* @return n!
*/
public static long factorial(int n) {
return n < 2 ? 1 : n * factorial(n - 1);
}
/**
* it computes the number of combinaison C_n^p.
* The function is only recursive and do not use an array to store temporary results
*
* @param n max cardinality
* @param p sub cardinality
* @return n among k combinations
*/
public static int combinaison(int n, int p) {
if (n == p) {
return 1;
} else if (p == 0) {
return 1;
} else if (p == 1) {
return n;
} else {
return combinaison(n - 1, p) + combinaison(n - 1, p - 1);
}
}
/**
* @param x a value
* @return true if x is power of 2.
*/
public static boolean isPowerOfTwo(int x) {
return (x & (x - 1)) == 0;
}
/**
* Returns the value of the first argument raised to the power of the
* second argument. See {@link Math#pow(double, double)} for special cases.
* @param value value
* @param exp exponent
* @return the power result
*/
public static int pow(int value, int exp) {
return value == 2 && exp >= 0 ? 1 << exp : (int) Math.pow(value, exp);
}
public static double log(double value, double exponent) {
return Math.log(value) / Math.log(exponent);
}
/**
* a rounded logarithm to avoid issues with jvm dependant math functions
*/
public static double roundedLog(double value, double exponent) {
return Math.round(log(value, exponent) * ROUNDED_LOG_PRECISION) / ROUNDED_LOG_PRECISION;
}
/**
* Returns the sum of elements in values from position begin (inclusive) to position end (exclusive).
* @param values array of ints
* @param begin starting position (inclusive)
* @param end ending position (exclusive)
* @return the sum of elements in values from position begin (inclusive) to position end (exclusive).
*/
public static int sum(int[] values, int begin, int end) {
int s = 0;
for (int i = begin; i < end; i++) {
s += values[i];
}
return s;
}
/**
* Returns the sum of elements in values from position begin (inclusive) to values.length.
* @param values array of ints
* @param begin starting position (inclusive)
* @return the sum of elements in values from position begin (inclusive) to values.length.
*/
public static int sumFrom(int[] values, int begin) {
return sum(values, begin, values.length);
}
/**
* Returns the sum of elements in values from position 0 (inclusive) to position end (exclusive).
* @param values array of ints
* @param end ending position (exclusive)
* @return the sum of elements in values from position 0 (inclusive) to position end (exclusive).
*/
public static int sumTo(int[] values, int end) {
return sum(values, 0, end);
}
/**
* Returns the sum of elements in values.
* @param values array of ints
* @return the sum of elements in values.
*/
public static int sum(int[] values) {
return sum(values, 0, values.length);
}
/**
* Retuns the sum of elements in values.
* @param values matrix of ints
* @return the sum of elements in values.
*/
public static int sum(int[][] values) {
int s = 0;
for (int[] value : values) {
for (int j = 0; j < value.length; j++) {
s += value[j];
}
}
return s;
}
/**
* Returns the element with the greatest value in values.
* @param values array of ints
* @return the element with the greatest value in values.
*/
public static int max(int[] values) {
int max = Integer.MIN_VALUE;
for (int value : values) {
if (value > max) {
max = value;
}
}
return max;
}
/**
* Returns the element with the greatest value in values.
* @param values array of ints
* @return the element with the greatest value in values.
*/
public static int max(int[][] values) {
int max = Integer.MIN_VALUE;
for (int[] value : values) {
for (int j = 0; j < value.length; j++) {
if (value[j] > max) {
max = value[j];
}
}
}
return max;
}
/**
* Returns the element with the smallest value in values.
* @param values array of ints
* @return the element with the smallest value in values.
*/
public static int min(int[] values) {
int min = Integer.MAX_VALUE;
for (int value : values) {
if (value < min) {
min = value;
}
}
return min;
}
/**
* Returns the element with the smallest value in values.
* @param values array of ints
* @return the element with the smallest value in values.
*/
public static int min(int[][] values) {
int min = Integer.MAX_VALUE;
for (int[] value : values) {
for (int j = 0; j < value.length; j++) {
if (value[j] < min) {
min = value[j];
}
}
}
return min;
}
/**
* Returns the largest (closest to positive infinity) {@code int} value that is less than or equal to a/b.
* Adapted from {@link Math#floorDiv(int, int)}.
* @param x the dividend
* @param y the divisor
* @return the largest (closest to positive infinity) {@code int} value that is less than or equal to a/b.
*/
public static int divFloor(int x, int y) {
if (y == 0) {
return Integer.MAX_VALUE;
} else {
return Math.floorDiv(x,y);
}
}
/**
* Returns the smallest (closest to positive infinity) {@code int} value that is greater or equal to a/b.
* Adapted from {@link Math#floorDiv(int, int)}.
* @param x the dividend
* @param y the divisor
* @return the smallest (closest to positive infinity) {@code int} value that is greater or equal to a/b.
*/
public static int divCeil(int x, int y) {
if (y == 0) {
return Integer.MIN_VALUE;
} else {
int r = x / y;
// // if the signs are the same and modulo not zero, round up
if ((x ^ y) > 0 && (r * y != x)) {
r++;
}
return r;
}
}
/**
* Returns the sum of its arguments,
* returning either {@link Integer#MAX_VALUE} if the result overflows an {@code int},
* or {@link Integer#MIN_VALUE} if the result underflows an {@code int}, .
*
* @param x the first value
* @param y the second value
* @return the result
*/
public static int safeAdd(int x, int y){
int r = x + y;
// HD 2-12 Overflow iff both arguments have the opposite sign of the result
if (((x ^ r) & (y ^ r)) < 0) {
long rr = (long)x + y;
return rr > 0 ? Integer.MAX_VALUE:Integer.MIN_VALUE;
}
return r;
}
/**
* Returns the difference of its arguments,
* returning either {@link Integer#MAX_VALUE} if the result overflows an {@code int},
* or {@link Integer#MIN_VALUE} if the result underflows an {@code int}, .
*
* @param x the first value
* @param y the second value
* @return the result
*/
public static int safeSubstract(int x, int y){
int r = x - y;
// HD 2-12 Overflow iff both arguments have the opposite sign of the result
if (((x ^ y) & (x ^ r)) < 0) {
long rr = (long)x - y;
return rr > 0 ? Integer.MAX_VALUE:Integer.MIN_VALUE;
}
return r;
}
/**
* Returns the product of its arguments,
* returning either {@link Integer#MAX_VALUE} if the result overflows an {@code int},
* or {@link Integer#MIN_VALUE} if the result underflows an {@code int}, .
*
* @param x the first value
* @param y the second value
* @return the result
*/
public static int safeMultiply(int x, int y){
long r = (long)x * (long)y;
// HD 2-12 Overflow iff both arguments have the opposite sign of the result
if ((int)r != r) {
return r > 0 ? Integer.MAX_VALUE:Integer.MIN_VALUE;
}
return (int)r;
}
/**
* @param x long to cast
* @return the closest int value when safe casting a long into an int
*/
public static int safeCast(long x){
if(x > Integer.MAX_VALUE)return Integer.MAX_VALUE;
if(x < Integer.MIN_VALUE)return Integer.MIN_VALUE;
return (int) x;
}
public static double log2(double a){
return Math.log10(a) / LOG10_2;
}
/**
* @param n a long value
* @return true if n is a perfect square, false otherwise.
*/
public static boolean isPerfectSquare(long n) {
if (n < 0) {
return false;
}
switch ((int) (n & 0xF)) {
case 0:
case 1:
case 4:
case 9:
long tst = (long) Math.sqrt(n);
return tst * tst == n;
default:
return false;
}
}
}