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/*
* Copyright (C) 2011 The Guava Authors
*
* Licensed 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 com.google.common.math;
import static com.google.common.math.MathPreconditions.checkNoOverflow;
import static com.google.common.math.MathPreconditions.checkNonNegative;
import com.google.common.annotations.Beta;
import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.VisibleForTesting;
/**
* A class for arithmetic on values of type {@code int}. Where possible, methods are defined and
* named analogously to their {@code BigInteger} counterparts.
*
* <p>The implementations of many methods in this class are based on material from Henry S. Warren,
* Jr.'s <i>Hacker's Delight</i>, (Addison Wesley, 2002).
*
* <p>Similar functionality for {@code long} and for {@link BigInteger} can be found in
* {@link LongMath} and {@link BigIntegerMath} respectively. For other common operations on
* {@code int} values, see {@link com.google.common.primitives.Ints}.
*
* @author Louis Wasserman
* @since 11.0
*/
@Beta
@GwtCompatible(emulated = true)
public final class IntMath {
// NOTE: Whenever both tests are cheap and functional, it's faster to use &, | instead of &&, ||
/**
* Returns {@code true} if {@code x} represents a power of two.
*
* <p>This differs from {@code Integer.bitCount(x) == 1}, because
* {@code Integer.bitCount(Integer.MIN_VALUE) == 1}, but {@link Integer#MIN_VALUE} is not a power
* of two.
*/
public static boolean isPowerOfTwo(int x) {
return x > 0 & (x & (x - 1)) == 0;
}
/** The biggest half power of two that can fit in an unsigned int. */
@VisibleForTesting static final int MAX_POWER_OF_SQRT2_UNSIGNED = 0xB504F333;
private static int log10Floor(int x) {
for (int i = 1; i < POWERS_OF_10.length; i++) {
if (x < POWERS_OF_10[i]) {
return i - 1;
}
}
return POWERS_OF_10.length - 1;
}
@VisibleForTesting static final int[] POWERS_OF_10 =
{1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
// HALF_POWERS_OF_10[i] = largest int less than 10^(i + 0.5)
@VisibleForTesting static final int[] HALF_POWERS_OF_10 =
{3, 31, 316, 3162, 31622, 316227, 3162277, 31622776, 316227766, Integer.MAX_VALUE};
private static int sqrtFloor(int x) {
// There is no loss of precision in converting an int to a double, according to
// http://java.sun.com/docs/books/jls/third_edition/html/conversions.html#5.1.2
return (int) Math.sqrt(x);
}
/**
* Returns {@code x mod m}. This differs from {@code x % m} in that it always returns a
* non-negative result.
*
* <p>For example:<pre> {@code
*
* mod(7, 4) == 3
* mod(-7, 4) == 1
* mod(-1, 4) == 3
* mod(-8, 4) == 0
* mod(8, 4) == 0}</pre>
*
* @throws ArithmeticException if {@code m <= 0}
*/
public static int mod(int x, int m) {
if (m <= 0) {
throw new ArithmeticException("Modulus " + m + " must be > 0");
}
int result = x % m;
return (result >= 0) ? result : result + m;
}
/**
* Returns the greatest common divisor of {@code a, b}. Returns {@code 0} if
* {@code a == 0 && b == 0}.
*
* @throws IllegalArgumentException if {@code a < 0} or {@code b < 0}
*/
public static int gcd(int a, int b) {
/*
* The reason we require both arguments to be >= 0 is because otherwise, what do you return on
* gcd(0, Integer.MIN_VALUE)? BigInteger.gcd would return positive 2^31, but positive 2^31
* isn't an int.
*/
checkNonNegative("a", a);
checkNonNegative("b", b);
// The simple Euclidean algorithm is the fastest for ints, and is easily the most readable.
while (b != 0) {
int t = b;
b = a % b;
a = t;
}
return a;
}
/**
* Returns the sum of {@code a} and {@code b}, provided it does not overflow.
*
* @throws ArithmeticException if {@code a + b} overflows in signed {@code int} arithmetic
*/
public static int checkedAdd(int a, int b) {
long result = (long) a + b;
checkNoOverflow(result == (int) result);
return (int) result;
}
/**
* Returns the difference of {@code a} and {@code b}, provided it does not overflow.
*
* @throws ArithmeticException if {@code a - b} overflows in signed {@code int} arithmetic
*/
public static int checkedSubtract(int a, int b) {
long result = (long) a - b;
checkNoOverflow(result == (int) result);
return (int) result;
}
/**
* Returns the product of {@code a} and {@code b}, provided it does not overflow.
*
* @throws ArithmeticException if {@code a * b} overflows in signed {@code int} arithmetic
*/
public static int checkedMultiply(int a, int b) {
long result = (long) a * b;
checkNoOverflow(result == (int) result);
return (int) result;
}
@VisibleForTesting static final int FLOOR_SQRT_MAX_INT = 46340;
static final int[] FACTORIALS = {
1,
1,
1 * 2,
1 * 2 * 3,
1 * 2 * 3 * 4,
1 * 2 * 3 * 4 * 5,
1 * 2 * 3 * 4 * 5 * 6,
1 * 2 * 3 * 4 * 5 * 6 * 7,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12};
// binomial(BIGGEST_BINOMIALS[k], k) fits in an int, but not binomial(BIGGEST_BINOMIALS[k]+1,k).
@VisibleForTesting static int[] BIGGEST_BINOMIALS = {
Integer.MAX_VALUE,
Integer.MAX_VALUE,
65536,
2345,
477,
193,
110,
75,
58,
49,
43,
39,
37,
35,
34,
34,
33
};
private IntMath() {}
}
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